Cabs aren't cheap there. The 'dillo is a free bus that works downtown and its pretty good transport, especially between downtown and campus.
I say rent a car. Rush hour sucks, especially on Mopac (loop 1) but its not the end of the world. You'll want to see a show at Stubbs, you'll want to experience 6th street. East 6th (or as we Austin bartenders used to call it - Dirty 6th) is chock full of bars where younger folks hang out. West 6th is really up-and-coming for the 25-up crowd. There are some very nice bars over there. Molotov has a ton of hot chicks because the owner is Chad Womack of "The Bachelor" fame. Annies West is a great place where I used to work, and just across the street behind Gatti's Pizza is Kung Fu Saloon owned by the same guys. Look for Nick or Ben and tell them that Curtis said you could have a free drink. Nick will probably let you drink free all night. Ben will probably say, "tell Curtis to go berkeley himself", then laugh and turn back to the 6 impossibly hot women that are surrounding him.
There are some neat hangouts on West 4th and 5th as well. Halcyon is a great coffee shop by day, Hipster bar by night. Next door at Pesce they have a great outdoor stage with live music most nights. Across the street are a couple cool gay hangouts. Whatever you do, if you see the name Mandy Lauderdale performing, GO SEE IT. She's my bestie and she puts on one helluva cabaret act. You might end up duct-taped to a chair with lipstick on your face, but its worth it. Get a message to her that you're friends with Curtis and you'll get picked out of the crowd for healthy humiliation for sure.
You'll want to make the 20 minute trip to Dripping Springs to get your BBQ. Salt Lick BBQ is legendary and very quaint. The Oasis out by lake Travis is another good landmark. The food is very good and you sit out on a terrace overlooking the lake. Go at sunset.
The other excellent BBQ places I would recommend are Rudy's (several locations) and Bone Daddys. Rudys is kinda cafeteria style where you order stuff by the pound. Bone Daddys is like Hooters but the girls are hotter and the food is really awesome. Get the "flying pig" sandwich. Its pulled pork, sausage, ham, and bacon on a roll. Its worth the heart attack.
If you have a time with nothing to do, Alamo Drafthouse (also several locations) is a neat experience. Its a movie theater that serves food and beer. Imagine a regular movie theater with every other row of seats removed and replaced with tables. They have all the normal new releases but also have special events, like Rocky Horror Picture Show with special guest Tim Curry.
Saltgrass is another good restaurant chain down there. Its a steakhouse kinda thing.
Zilker Park is a neat thing to see. Barton springs are there and they made it into a public swimming area. If you're into science, they have a very small tour talking about the local geology, the Barton Springs Salamander, and some other neat stuff.
If you're into shopping, there is a Cabela's about 20 miles south, and a very large outlet center in San Marcos about 50 miles south. And... while you're making that trip, do yourself a favor and visit two awesome towns; Greune (pronounced "green") and Wimberly. Both are incredibly charming.
South Congress is a fun experience. Lots of neat shops, curios, restaurants, and a trailer park that has nothing but catering trailers with the neatest snacks. Head down there around sunset and watch the Bats from the Congress bridge. They won't be plentiful right now, but the Congress Bridge is home to the largest colony of brown bats anywhere. Seeing the constant flow of millions of bats flying into the night sky is pretty awesome.
Visit an Amy's Ice Cream. Its an Austin original. Its kinda like a Coldstone Creamery where they mix in your toppings on a marble slab, but they have such interesting flavors including some alcoholic ice cream.
If I think of more I'll post them later. Right now my brain is empty.
