I think the ideas above to pick a place near a VA is great since that’s what you plan on using for health care. If you go on each medical centers website you can also see where they have clinics, which gives you even more options of potential towns.
I grew up near LaCrosse, WI which is about an hour from the Tomah VA and has one of the VA clinics affiliated with that medical center. LaCrosse is pretty, has a nice downtown, and is a university town. In the summer, you can go fishing, kayaking, boating on the river and there is a nice riverfront Park. Anywhere around Tomah or LaCrosse you will probably need one car, although if you live in town you could do more walking/biking and have a beater car for the few driving trips. I don’t know much about the Tomah VA but FYI they did have a “candyland” scandal a few years ago; overprescribing opioids. You could find a fixer upper in city center for under 100k, but average for a small 3bed is probably closer to 150k.
I visited St. Cloud, MN for a couple days for work and I thought it was a very nice small, university town next to a river. I was surprised that it actually had a downtown area. (Too many small Midwest towns don’t.) It also has a VA Medical Center and is only an hour from Minneapolis/St. Paul (where there is a larger VA Healthcare System). A quick search shows St. Cloud has many houses in the city center for 100k.
Not sure how far away from people you want to be. If you’re in a big city now, I suspect the city center of these small university or any city in the 20-50k population range will still feel like you have way more space and no crowds. But also for most of the smaller cities in Midwestyou can be out in the country within a 10-15 drive of a city if that’s the direction your looking at.
I think a family of four living off your military disability alone would be doable in these towns and the ones suggested below, but uncomfortably tight. If you saved enough to outright buy a house 100-150k house in one of these towns, then not having a mortgage gives you the breathing room to make living on 24k comfortable. Check out the MMM’s 2015/2016 spending for ideas. (He has more like these for prior years that are lower.)
https://www.mrmoneymustache.com/2017/05/19/2016-spending/ You can mimic a 24k lifestyle now to see how you like it. Pick a potential place for FIRE and calculate your housing (Mortgage, Interest, Property Taxes, Insurance, heat, electric, water, sewage, garbage, and 1% of house price maintenance fund) and transport costs (car loan if any, insurance, registration, fuel, maintenance, replacement fund). Subtract that from your 24k. Then use that amount to set your current non-housing/transport budget. Evaluate how easy/difficult it is for your family. Bonus: if this is less than what you spend now, then more savings goes towards your FIRE funds in the meanwhile.