Well, my time to chime in.
As a RPG-writer, I've stumbled with how would my mermaids culture and architecture look for humans. Well, unless your mermaids and your humans are isolated, some things will follow, but the more important one is:
Mermaids won't live in deep waters
As a human-sized fish-mammal hybrid, mermaids are not adapted to living in deep water conditions. They will probably live around beaches, and maybe a bit off the coast, but never on deep, empty ocean. The human body that makes their upper torso doesn't support deep-sea living for long without heavy equipment, and evolution can only take you so far as adaptation goes without making them look like whales or sea-lions. The sea can be really cold, so they will need shallower, warmer waters to thrive. Also, in literature, at least, mermaids go with some frequency to the surface to interact with the surface in a way or another. Don't think of them like the mermaids from the Disney movies or as friends of Aquaman. They are likely to spend a lot of time on land trading, gathering stuff from the beaches, getting sun-baths, luring sailors to eat them alive... mermaid stuff. They are half-human, and they can breath air. They will probably love the warm sun on their skin, the taste of fresh coconuts, or some freshly-cut palmito with their fish. They will love to look to the sky at full moon, and will probably love to sing in the beach, around a fire. You can't sing really well underwater.
I believe that mermaids would start more tribal than humans, at first, like Amazonian or African tribes that develop a bit away from the main bodies of civilization. They will probably be more carnivorous than anything else, since fish is a way better source of fundamental nutrients for mammals of their size than kelp - I imagine their diet being similar to those of dolphins. Since building stuff underwater is hard, mermaids will probably be stuck with living in caves or some rudimentary rock-houses for a while.
That's it, until they see what land-dwellers built.
At the moment the mermaid scouts bring the notice of the majestic human cities near the coast, I believe mermaids will take a great deal of interest on those strange, two-legged creatures and the stuff they build. Their leaders will want those majestic buildings, too, and will, sooner or later, do what humans do best - imitate them.
They will try to simulate what they see on the coast, with their vision on how should things work on their culture. They will probably build hybrid constructions on relatively shallow water, with some parts over and some parts under water. However, this type of building needs materials that are really hard to get underwater, so they will probably need to buy them from land-dwellers. To make that work, your mermaids will need some economical advantage over humans - something that only they can get, it's expensive, and that humans really want. That way, they can buy the materials and hire the work they need to build their coastal palaces, which will be built using granite and similar materials, and adorned with gold and gemstones. Mermaids like some bling, too. Those buildings will probably be made to be used by mermaids, with some capabilities for humans to cross. There is no good to have a sublime palace if you can't show it off to the other people.
Mermaids will probably love wide open spaces, with tons of glass panes for light to shine in, probably emulating how the sun shines through the water. If they do have multi-store buildings over-water, they will use columns of water which connect pools in different floors to go up and down. Those columns could be partially sealed off to prevent water spill, and some crafty use of wind-powered water pumps will make sure the water stays on level everywhere.
The use of hybrid buildings will make a lot of things that are harder underwater way easier. Medical care, for example. If blood spills on land, it goes down to the ground and stays there. If it spills underwater, it goes everywhere, mixing with water and making things really messy. Metalworking and leather working simply don't happen underwater, and so your mermaids will want some surface area to work with those the same way humans do.
Also, electricity and water can go messy really fast, so they will probably be way more wary of electrical power than humans are. If they adopt it, it probably will be restricted to the surface areas of their dwellings, and will not, for obvious reasons, extend to their underwater areas except on some really, really controlled settings for essential stuff - mostly illumination and heating.
So, in essence, instead of deep-water cities, they will probably build coastal, resort-like cities adapted both for them and for humans, which they will probably be contacting often. Their cities will probably be build from the beach towards the sea, and will extend for a while until the water gets too deep to build or too cold to live in.
As a side-note, don't be afraid to build a less-advanced culture for your mermaids. Their problems and environments are different, and so will be their development.
Think of how Hawaii was before the arrival of the foreign people, and how it is now. Seems as a good way to go with your mermaids, I think.
Most important of all, don't let their fish-tails be something restrictive. On the contrary, use them to boost their capabilities, and let them roam the land and the sea in ways that we humans can only dream of. Don't shackle them to the bottom of the ocean. Their voices deserve to be heard, their songs deserve to be listened, and their belies deserve to be full of sailor-meat!