I'd also recommend hitting many of the local breweries, Austin has had an explosion of them in recent years. A good one for a touristy stop is the Oasis Brewing Company, they are on a deck overlooking Lake Travis and have a great view. Their beer isn't my favorite, but that view is the best on the lake. Adjacent you will find the Oasis restaurant, with similarly great views and decks. AVOID! The food is not good. You're better off with a beer and food from the brewery, or eating elsewhere.
For a day trip or activity consider Hamilton Pool, or hiking / biking at one of the many parks in the area (Pace Bend, Mulshoe,McKinney Falls, the Greenbelt - right in the city, Enchanted Rock, Pedernales Falls, Inks Lake). Note that Hamilton Pool requires advance reservations and fills up way in advance.
Austin is more of a eating, drinking, outdoor activity sort of city than a sightseeing city. That said, some examples of touristy stuff to see/do would be touring the Capital building, walking the UT campus, the Lady Bird lake (aka Town Lake) hike and bike trail, lounging around Zilker Park, Barton Springs (swimming), scenic overlooks at Mount Bonnell and the Pennybacker bridge, the Bob Bullock Texas State history museum, LBJ library, Lady Bird Wildflower center.