I like the Austin Motel, Jay. It's a little kitchy, but it's in a good area for doing things on foot, and is a very 'Austin' place to stay. It's what I would recommend to someone coming to the area for the first time.
There are plenty of restaurants, coffeeshops, bars and music venues right there on Congress Ave, and you can hop a 'Dillo (the cheap shuttle bus) to go right into the heart of downtown in less than 10 minutes without having to worry about a designated driver or finding a cab.
Hyde Park is fine, nice and central, but you will need to cab or regular bus to get to the bulk of the nightlife.
Honestly, anything that you rent central is probably going to be plenty safe. Some people might say not to go east of I-35, but I've been out there plenty on foot and on bike and have never had a problem.