UT has an excellent shuttle bus system. If you want to live car free in Austin you need to make it as easy as possible for your GF, so look at places where a UT shuttle bus route runs right to the campus location nearest your GF's major department.
When you've selected the best UT shuttle bus route, find a location which is near a grocery store. The biggest grocery chains in Austin are HEB and Randall's.
When you've found a good candidate location, verify that it's near a Capital Metro bus route. Ideally you'll want to be near one of their transit centers. All buses here have racks for two bikes. This is a major convenience if you really intend to be car free. To guarantee that there's a space on the rack for your bike, try to catch inward bound buses at the far end of their routes.
Personally, I like to cycle on the south, east and north sides of Austin. The west side has prettier views but the grades are steep and there are fewer road choices (i.e., you're often forced onto scary arterials).
An example neighborhood that women tend to like is just west of Loop 1 at Far West Blvd. Short walk to a grocery store & lots of retail, on a UT shuttle route, on a couple of Capital Metro routes, easy bike crossing of Loop 1 over to Shoal Creek Blvd (which is the bike route of choice in that area). Condo and apartment prices not too expensive there. Easy access to the western hills if you like that kind of recreational riding.
There are numerous other neighborhoods where it would be possible to live car free in Austin.