We are definitely not that regulated. Nothing like what you're used to lol.
As far as the SFH - $400k opens up most of the city with your requirements. If you look at the city on a map the major "areas" of Jax are separated by the Saint Johns River- the southeast quadrant of Jax is the most desirable, and priced accordingly. The closer you get to the ocean, the higher the prices. North of the river is North side. West is west side. Both North side and West side have some rough areas as well as newly developing areas, and then it fades to rural country once you go north and west enough. I personally feel Westside offers the best values in Jax, as it is still very affordable but growing quickly. If you look at the 295 corridor (except for SE Jax which is very developed all over), as a general rule once you step out of that circle, you are further from amenities and heading to the country.
Downtown is pretty much our worst area. When you see the low prices there, there's a reason why. Unless you're ready to deal w crime/drugs/rundown neighborhoods/questionable characters you will want to go further out.
The thing w Jax that you wont be used to, is that the areas are so mixed. You will see an old trailer on an overgrown lot, next to a beautiful newly constructed subdivision. Neighborhoods are not well defined geographically nor can you categorize well by zip codes or school districts, like you can up there. You just kind of get to know the areas over time.
I just checked and there are extremely few 20-100 unit MFs. Same rule of areas applies here. I also think you will have trouble finding MFs that size that are newer than 1980. Most of what I've seen like that is older, and very often you will have an investor selling a bundle of singles/duplexes/quads together, rather than one complex.
I feel like I'm starting to write a novel here lol, and I could go on. If you are coming down, spend a few days driving around and looking at the different areas. Certainly feel free to reach out to me if you have more specific questions, or need any more help.