I have friends who live in uptown,right smack in the middle of westvillage, the apts are made so it's easy to room, they pay 700 each,(just two of them), and it's pretty close to utsw, the immediate area around isn't that safe a place so most people try to live a bit away.
I know some people who work at utsw and live in the village,it's about 5-10 minutes away from the best places to hang. but 20 minutes from utsw, and depending on which community you live in either dirt cheap or fairly expensive, the westside and northbridge are the more expensive, but some are in the middle.
Closer to utsw, try the cityville apartments.they're new and very nice.
what's your budget?