The Edge on or about 4th and Indiana is nice. It is north of campus (opposite end from the law school), and a little removed from the rest of the town, but it is new, the units are pretty nice, and they only allow grad students. A good number of law students live there. Price is probably close to the limit of your range, if not a bit over, making it among the most expensive places in town.
Dominion on 50th is another decent option, but don't sign a lease over one year, they make it impossible to break your lease or sublease. A few old, still nice. Also on the high end of your price range.
Bear Flats and Jackson Square are near the school off of 19th and Quaker. They are older, but appear nicely remolded and well-kept. I haven't been inside either, but I drive by each almost everyday on the way to the gym, and they look very nice. Pictures online of the interior also look nice. They are a bit cheaper that the other two.
Quail Creek and Las Colinas are both south near or outside of the loop. They are older, have a few more crime issues, but are cheap and offer law school discounts of $100 a month on some units. A lot of the married law students seem to live here, but also single ones.
There are numerous other options, but these are the places that I know have sizable law student populations living there.
Other than that, some basic geographic rules:
-The farther east of University, the worse things get. Once you hit I-27, you've gone too far east (too dangerous past this point). I wouldn't go much north of 4th Street. Go as far south and/or west as you want, but the farther you go, the longer your drive will be. There seem to be a lot of complexes around the loop, generally in the Slide and 50th-60th area, and then all along the south loop. Taking a gander at google maps will help you conceptualize all this very quickly.
Good luck finding a place, and good luck in school!