I'm a 4th year undergrad at UVa and here's the breakdown on apartments . . .
You can live far(ish) away (and by this I mean a few miles) and have pretty reasonable rents. I'm in a pretty nice 3 bedroom at Eagles Landing apartments and we each pay $420/month, cable included. The problem with this is parking is a hassel. Figure $300/year to park at the stadium and take a bus or a 15 minute walk to the med center. You can park near the basketball arena for much less but the bus ride is longer. Then there's always get to campus early (before most hospital staff) and nab a street spot on Jefferson Park Ave for free.
Option B is to live on Jefferson Park Ave or near 14th street. JPA apartments tend to have parking readily available but can get pricey. I don't have any firm prices except a 4 bedroom 2 bath at 1815 JPA (nice, new building) is something like $1750/month + utilities. But it's possible you could find a nice 2 bedroom for $900ish/month. Of course there are many houses for rent that are dumps with like 5 bedrooms that a bunch of people can cram into.
Now, 14th street is off "the corner" the little bar area near the med center. This area can be moderately pricey and places tend not to be as nice, but you are really close to the med center and bars/restaurants, parking is extremely limited tho and can be a real hassel.
Guess that's about all I can suggest. If you want to look at spec complexes a little further away, Eagles Landing, Jefferson Ridge, and Sterling are all along Old Lynchburg near 5th street, approx 2 miles from campus. Closer to campus check out 1800 JPA or 1815 JPA (if you can find some more roommates). Not as sure about 14th street area apartments.