First tip: Go to San Antonio instead
Seriously, avoid 6th Street downtown. Try the Warehouse District (4th). Definitely rent a car, because you will quickly want to venture out of the downtown area after hitting Lady Bird lake. Sample some eateries on Barton Springs and hit Zilker Park. But honestly I wouldn't stay in a hotel downtown or anywhere close to the downtown area.
South Austin also has some cool spots, as does South Congress (SoCo). A little north, spend a day at The Domain.
Hula Hut and Mozart's on Lake Austin, The Oasis on Lake Travis, all popular tourist destinations. Venture out into the Hill Country on 290 or 71 and stop at a winery or two.
Be prepared for traffic. And extremely high prices. It's getting nuts around here.