Having attended the UT Austin for several of my many years on this earth, I have a few observations.
Most of the hills in central Austin are short. The steeper they are, the shorter. Gears are helpful but not absolutely essential, I spent about a year commuting to campus on a single speed. I've gone up the MLK/Lamar hill on a vintage 3-speed. A year of riding the same route will make you fit for it no matter what you ride, and by and large if you're living within 3 miles of campus (from North Loop/Koenig in the north to Pleasant Valley/Chestnut in the East) you can make it with pretty much any bike that has handlebars and air in the tires. If you live further, like at Riverside or Far West, you should start looking at issues like weight, aerodynamics, and carrying. Do yourself a favor and get a rack. It got to 109 in Austin yesterday, and it'll stay in the 100's and upper 90's through September and sometimes into October. Sweating season is 9 months out of the year, and having to wear a backpack full of books only makes it worse.
I recommend a used bike for commuting, either an early-to-mid 90's rigid MTB with slicks or a "ten-speed" road bike. As several other posters pointed out, they blend in well and have pretty nice ride quality.
The police impound bike auctions are not worth going to. The kinds of bikes they impound are the ones that people have left behind because they don't want them. They're that bad. If you can't adjust brakes, true wheels, replace a chain, adjust derailleurs, and patch tubes on your own, it'll cost a fair penny to get those bikes back in working order at a bike shop, and if you can do all those things, you're better off spending your efforts looking at bikes on Craigslist or one of the above mentioned BikesDirect bikes.
If you want to learn HOW to do your own maintenance, the big bike co-op in Austin is the Yellow Bike project, which requires you to take the 12 bus all they way east to Weberville Road. They teach skills, have spare parts, and even sell used bikes, mostly of the rigid MTB and "Ten-Speed" variety. If you're short on cash they have a volunteer-for-bike trade program (you can do it even if you're not short on cash).
Also, use a U-Lock. I always lock through my front wheel and frame. Don't even bother with cable locks. There's a good chance you'll have a bike or two stolen, but most of the bikes that I know have been stolen (including one of my one) were stolen from people's yards, not on campus. Store your bike inside, or at least in a secured back yard. My former roommate's bike was stolen when somebody ripped out the railing on our front porch that the bike had been attached to, in broad daylight.
Feel free to ask me more specific questions if you know where you'll be living, I can point you to some resources in your area and good routes to take.