You haven't said where you are now (country/state), so it's tough to recommend a place unless we know generally where you are.. NE? SE? Central US, desert SW? Big Sky country (MT/ND/SD)? Starbucks area (NW).. Land that shakes a lot.. Cali? Just picking a place on the map, without a means to get there isnt easy.
areas in and around Phoenix, for example, has some furnished studios and 1br apts btwn $520-$609, plus elec (btwn $40-$60/mo). If you don't mind a lil warmth for a few months.. you never have to shovel snow, slip on the ice, and monsoon season is only 6 to 10 weeks. Besides, a few of the nations BEST TG docs are here.
There's always Vegas.. and "what happens in Vegas.." well.. you know the rest.. 6 short hour drive.. Southern California.. think I'd avoid Texas.. I wouldn't think its that trans friendly.

The central states cost of living is fairly low.. but acceptance.. hmmm..

Wisconsin.. Milwaukee has some inexpensive areas, but is the opposite end of the thermometer from AZ

Portland is supposed to be one of the best trans-friendly cities in the US, but if you don't like rain..
If transportation is a problem (iffy car) Phoenix has decent bus/light rail (in town only) service but would take a while to get from one side of the Valley (surface) Of the Sun to the other.
You should be able to look up Apartment Finders (city) and see what's out there. Google search
http://www.bing.com/search?q=apartment+finders&qs=AS&pq=apartment+finders&sc=8-17&sp=1&FORM=IE11SR&src=IE-SearchBox and see what comes up.
Good luck!