This will depend on who is making the map, and why, in-universe.
Maps aren't accurate during most of this time period. Wildly so. Until the Age of Exploration began, accuracy simply wasn't a thing. You've already got some great answers here, going to add my spin on it.
Here are some points to consider
- Most villages would not bother with a map. Important cities, yes.
Tiny towns, not so much.
- Many maps were commissioned for important people--Kings, Lords, that sort of thing. They weren't really to help navigate, but for display. To learn what was in the world approximately.
- While the map might have everything known on it, it may not be accurate in the least.
How far from a village should I plot the "we do not know what is
there" line? (again, reminder: Classic medieval world with no magic
involved, fastest means of transportation is a horse)
The answer is it depends on who is making the map, what they know and what the person that commissioned it is asking for. Does the Lord want accuracy? A focus on the town? A map of THE KNOWN WORLD? Is this a map specifically sold to pilgrims of the pilgrim route? If so, then mapping the known world would not be the goal.
Paper is rare, so they'd have to have some level of education to be allowed to try making it.
Most people in England know about London, even if they are far, far away. So let's take that example. If your village is 300 miles away from London, the people there would have still heard of it. Some few people in the village may have even travelled there.
So a somewhat educated fellow brought up in the church with a gift for drawing might be commissioned by the local lord. In this case they might detail their own town more than anything, and then set major cities where they know them to be. So York, London, any town above 3,000 they may have heard of, they would place on the map.
Of course, do not assume that the in-universe map is going to be accurate. It's pretty unlikely that it will be. Your map-maker might know that France is across the channel and where Ireland is, in theory, but it's unlikely that they've actually been.
Should I use geographical landmarks as "border of unknown"? E.g.: No one crossed that big river yet, so behind the river are woods and dragons live there
They would not necessarily place HERE THERE BE DRAGONS on a map like this. It's actually not as common as you might think. Instead, they would just assume land that they know, or vague mountains to fill in the space, placing cities where they believe them to be. (They might know that London is North of York, and that it's on the Thames, but they might not know the accurate shape of the coastline of England).
See, your map maker knows that there are places beyond. It's quite possible vaguely know of France, Italy, and Spain. How much they know about the distances between, where they actually are, will be based on descriptions in books they may have read (which will not be all that detailed, or could be interpreted a number of ways). They might not include all these on the map, but could have arrows pointing the way. The dragons and such that you see on some maps actually came later/at the end of Medieval period--and sometimes they were just decorative.
Mapmakers would often just talk to people, and they might know someone who knew someone who said there were dragons past the mountains up North. There's no real way to check on it, it's known though, so best put it on the map. Plus it creates visual interest, and mapmakers were as much artists as they were cartographers.
What are common reasons to stop discovering? Why would medieval person stop at a river/mountain and not go any further?
Is there anyone past the mountains that might buy what you're selling before it goes bad? No? Well, it's not worth the journey then.
Plenty of Medieval people never travelled more than 30 miles from their home. But there were also folks who made regular trips to large cities for trade and fairs. Also there were religious pilgrims, merchants, and some nobles who just liked to travel.
There were also jobs, like fishing, where you could get to know the coast intimately over a wide range. But good luck finding someone who is both educated enough to draw an accurate map and has that knowledge base or is willing to give up the secrets of their trade.
Sometimes a lord or king would even ask for someone to travel in order to make a map, if they were interested in exact distances of their kingdom.
The question you are asking is so...individual you're asking "why would a person" when people are very different. Why haven't you been to Indonesia? (well, mayhap you have) How do you KNOW it exists for certain?
Maps are largely made in this time, based not on personal experience, but on those who came before. The more detailed and accurate a map is, the more likely it is to be specific to a purpose (navigating the coast, the pilgrim road, a trading route with directions).