I have already returned to the USA and have a place. However I am looking for a cheap place to do winters in a milder climate. One place that keeps popping up is Macon, Georgia. From what I can see there are some cute homes that are a bit rough. The neighborhoods look pretty unkempt in some areas but now and again a really cute place pops up that looks actually decent, prices are very low.
I have asked about the crime and it is present though I was told it isn't gang infested, apparently it is a typical mid size southern town trying to make a come back. It has a historic downtown and actually some decent options for dining and entertainment.
This suggestion is more for somebody wanting a house under $100k I have no idea about apartments or rentals. If houses are cheap rentals should be cheap as well. I imagine you can get a house to rent for well under $1,000.
it is not too far from Atlanta either which is a town I like. I would try to find something in a river valley to get some hills which prevent tornadoes.
Weirton, WV would be another place with rents under $1,000 cheap gas, cheap pretty much everything. It is the closest town to where I live in the countryside. It is 100% safe, has a variety of restaurants and some big box shops. It is 30 minutes from Pittsburgh. Pittsburgh has some cultural activities and attractions although I haven't been there much. I hate the hills.
It gets really dreary in the winter, that is what wears on me more than the cold. If I didn't have a really nice property in the forest here I would probably not choose Weirton. It does have a decent hospital and good things about it but it isn't pretty. There are nice natural areas surrounding it though.
Right now Macon and a few towns in Mississippi are where I am focused. Again I am not doing the summers there. Macon I like the idea of for some forms of entertainment as boredom will become your worst enemy in much of the USA.