I'm looking for help hiding a small colony. Imagine a few families, definitely less than 100 people, living in a small community together hidden from the modern world. They use 19th Century technology and seek to remain hidden. Where in North America could this be possible? Assume that they work the land themselves and are self-sufficient.
Sounds like you are setting up something like what exists in M. Night Shyamalan's The Village which is set in Pennsyvania. I think something similar could be set up in any decent sized forest area. Buy a few hundred acres far from the closest town and hollow out a spot in the middle for your settlement. As long as no highways run too close to your land, you could probably even leave it unfenced. Just use the trees to block line of sight. I'd suggest something a little further south so that the winter's aren't horrible. Fighting northern winters with 19th century tech is not fun.
Hidden in plain sight:
You can't really stop people (at least the government, with satellites) from seeing your community without magic. If nothing else, the folks looking for pot fields will see you growing things in the woods and think you're hiding something. So you need to decide exactly WHAT you're planning to hide. Are you trying to conceal the physical town? Without building the town itself underground, in a historical place, then you can't hide the town. So I'd suggest you need to hide the community.
The Amish live a life just like what you're describing. They live a simple life in a low-tech way, without electricity, cars, etc. But even the Amish have a dependence on the outside for manufactured goods and markets. It's almost impossible to be totally isolated from your surroundings. So think about what it is that your community wants to hide, and specialize hiding that.
So some of these details will depend on exactly what you want to conceal. To physically isolate from the outside world, pick a small island in the middle of the great lakes. I'd go with some place like Beaver Island, which did, actually have such an attempted society. Several attempts have been made to establish insular communities or even independent countries on islands in the great lakes based on ideologies, religions, and such. People will sort-of know you're there, but if you choose to be detached, few people other than in a couple nearby harbors will know about you. With a cover story like, "We're an offshoot of the Mormons/Amish," people will know there are folks there, but that there isn't really anything to see. There are other island areas off of coasts that would provide a similar level of isolation.
Now you need to keep you own people from wanting to leave or know about the outside. Nothing will spread the word about your community like a few ex-members talking about sexual abuse and cult worshipping. What mechanism do you have to keep the members in place? Are they werewolves? Do they all speak a unique language? The physical isolation in the middle of a great lake helps, but someone determined enough WILL leave, and even in The Village, there came a time that someone needed to step outside the fold.
Indian reservation / Indian reserve
If you do not want to be found, you can be invisible. Or you can be in an area where people do not look and if they do they assume you are other than what you are. There are very large, very lightly populated tracts of land in North America where native tribes have sovereignty. The Navajo reservation in the US is immense. The linked source estimates 35% of Canada are Aboriginal lands (from the viewpoint of the Canadian government; from Aboriginal viewpoints, most of the country is unceded land).
Persons living in these area might not have to pay tax to state / local government. They might or might not have to pay tax to the native authorities overseeing the land.
I can imagine a scenario where your people live in a remote area in Canada on an Indian reserve. The tribal authority sort of knows some people are up there. They are not sure if they are natives or not. Those people cause no trouble and ask for nothing. The native authority has its hands full with events on their other lands, and so leave well enough alone. Maybe someone checks every couple of years.
The state and national authorities know even less. They might be aware there is a settlement because they see it by plane. They know it is on native lands and assume they are indians, and leave it at that.
In a comment to another answer you mentioned that your proposal was something like M. Night Shyamalan's "The Village." It would have to be, even to an extent greater than Shyamalan's movie.
It isn't just Google maps/Earth that's the problem. It's hikers and hunters and fishers and mushroom pickers and campers and real estate agents and their clients, and resource developers such as loggers and oil and minerals and... well... the list is very long.
While there are a great many square feet that have never felt the touch of a human foot, there are precious few (if any) square miles that haven't enjoyed the close scrutiny of humanity. And considering the history western civilization has had with small, isolated communities with a strong resentment for outside interference (frequently described as "cults"), it's hard to believe that the moment they were discovered (an inevitability, IMO, the point of this challenge) wasn't also the first day they would be analyzed with a microscope.
And to make things worse, we have drones. Big military drones. Small personal drones. Drones of all makes and models that can travel vast distances at great heights with pretty good cameras.
Your 19th century community would need to engage very, very 21st century legal and political acumen to retain their privacy and isolation. And the moment you allow that, it's really just a group of people pretending to live 19th century standards.
And once you allow that, they can be located almost anywhere in North America. Greater than 60% of the U.S. and probably more than 90% of Canada are rural to wilderness.
There are many instances of large communities living beneath the surface. The largest one I know of was the City of Derinkuyu in Turkey.
Locate the community in a rural area well away from highways or other communities. I would choose a dense, forested region as it will deter most humans. It will also work to obscure smoke from cooking/heating fires and make aerial detection by satellites and drones harder.
The community's largest difficulty will be growing food. As they would not want to farm above ground, they would need to have sunlight chimneys with mirrors and/or lenses to bring light to the subterranean fields. But still doable with 19th century technology.
Another potential difficulty is the fact that North America has a lot of comparatively hard rock. AFAIK, creating and expanding the community will take time and significant labor in most places with dense forests and may be hard to hide.
Living on an island...
As other answers have said, anywhere on the mainland risks discovery by random hikers, hunters, firefighters, BATF investigators, etc.. Of course you can kill them, but most of them will have told people where they were going, so their disapearance will guarantee some pretty good investigation within a 20 mile area of their last known location and either side of their expected track. In particular, there will be extensive use of helicopters and drones.
More likely would be an offshore community setting up shop on an island which is not too near major routes. Peter Benchley's novel The Island supposes exactly this situation (with pirates). Benchley's community is not fully self-sufficient, requiring regular looting of passing boats, but is reasonably close to it.
Piracy of course requires complete secrecy, so anyone encountering them either has to die or join them. A closed society though merely has to be unwelcoming and turn away visitors. If they only get the occasional lost yachtsman noticing them, word is unlikely to get out for some time. Naturally an aircraft overflying at a reasonably low altitude would see the crops, but it may not be anything they'd particularly comment on afterwards, and most aircraft won't be low enough to see much. It's hard to keep track of exactly which small islands are or aren't inhabited, after all, and some are only inhabited sporadically anyway.
Of course Google Earth will pick up this at some level of detail. Google tends only to use higher-resolution imagery on land though, so you won't be able to see too much; and for anyone to notice this community would require someone to intentionally find this island and zoom in. Eventually this might happen, but it's not that likely. This could even be a plot point for why your protagonist is the first person to find them.
They need outside protection
As others have noted, a farming village can't hope to remain undetected just keeping to themselves. So what they need is someone from wider society protecting them.
On the outside you have two options: Either you have a two-part cult (something like "The Innocents live a sheltered live, the Guardians serve them by shielding them."). Then the outside facing cult would be known, would own the land, would provide cover stories, would mostly adapt to modern life and would keep anyone away from the inside cult. In this variant, you may get away without the colony actually knowing.
The other option would be a really long lived notary office. The founder of your colony was really rich, set up an endowment and a contract with the notary office. They act on behalf of the actual owners of the land (the colony as a whole), handle all business with the outside world and keep everyone away. I think in this variant you definitely need someone on the inside knowing. While such a long-running contract seems plausible, the office would want to get in contact at least every decade or so. (This idea is adapted from "One Trillion Dollars", a novel by Andreas Eschbach.)
So on the inside it could be that the cult leader/mayor/priest/xatriarch is the only person with connections to the outside. (I mean, you anyway need a reason why no single person in 125 years ever left the village, so you might as well work in this exception.) There are regular 1:1 meetings and the "ambassador" role is handed down from generation to generation. The ambassador keeps a secret what they actually do when they go into the woods alone every new moon (or whatever).
Central/Eastern Alaskan wilderness.
Your community will need to identify a large tract of private, undeveloped, forested land with access to water that they know the land-owner never visits. Given that, in certain parts of Alaska, the community will be quite remote and will generally be left alone. Hunting, fishing and basic agriculture done without clearing trees could sustain them without showing a large satellite footprint. Winters will be brutal. Keeping them completely unknown to the county government would be a challenge, but with careful construction of disguised dwellings, or perhaps living in a cave, in the midst of a vast territory, it is not unthinkable. Individuals would probably be seen from time to time, but could explain themselves as hikers or tourists.
Frame challenge: Such a colony might die out quickly
Such a small community will have a hard time sparing the calories to feed just a smith.
If the smith dies, or his (single) apprentice is inept, the colony won't make it even into the second generation.
They'll also have no buffer to survive any disaster.
A single bad harvest would force them to give up or die. And a bad harvest can have many causes: Weather, flooding, a horde of wild boars devastating your fields, plant diseases and plant parasites.
They could live as hunters, but then there would be good years and bad years.
The one risk that couldn't be eliminated at all would be human diseases; these can easily kill 10-90% of the population, and below a certain threshold, the colony just isn't viable anymore. (Plus many diseases leave their victims enfeebled, so they can't gather the resources to survive the next winter.)
Long-term, inbreeding will most likely make the colony fail.
It's not very likely to happen in the 1900-today timeframe, but it could be a plot device if some colonist somehow finds out (or knows from pre-colony education) that the general consensus is that a human colony needs roughly 1000 members or more to avoid inbreeding. 100 is far too few for any long-term plans, so the founders would have to be either ignorant, or planned to go out of isolation within a few decades, or have started with 1000 persons but some disaster struckt.
A strongly appealing scenario for perhaps many people. Hope there are many such communities already out there. Agree that a fully non contact community has a struggle with resources, gene pool, and for most, hard to be long lasting. Have mildly considered similar idea in Australia, set up perhaps in 1840's, and inventing own steam 'gothic' technology. Explored local mountain area and found a few very good sites, one of them showing faint traces of previous long term 'camping'. In a mountain area could always show up as cloud covered spot on mountain in Google Earth, using a cloud generating device. Much of it could be underground. Contact with modern world may not be a problem, just the benefit of a counter cultural refuge. Possible to have PV cells just looking like natural rock etc. Vent for fire in cave, could look like a campers fire just left smoking. Of course if somebody or govt gets suspicious may be difficult to avoid detection, but for most of time nobody is looking.