I think the two best places to look for an apartment or house are in South Austin or in Hyde Park. South Austin has a lot of cool bars/live music venues real near by - if you have a bike, you can ride it everywhere and not spend money on gas. Also, Barton Springs is nearby and it's not a bad walk to downtown on the weekends. Hyde Park has great restaurants and smaller dive places like The Parlor to hang out in. Both areas have bus lines that are pretty reliable and run every 15-20 minutes.