A few ideas:
- Austin bills itself as the live music capital of the world. There are tons of places downtown with live music. Just be careful. 6th Street gets sketchy after 11pm or so. Do your homework in advance. Stubb's is a BBQ restaurant that also has live music. The BBQ is good, not Austin's best, but you can kill two birds with one stone there.
- Rent a paddle board, kayak, or canoe and row up and down Lady Bird Lake (previously called Town Lake). Great views of downtown. There are tons of places to rent these items along the lake.
- Head to Mount Bonnell. It's a hill, not a mountain, but the views of Austin are fantastic. Added bonus, there is a Mormon reference on the plaque at the base of the trail. The hike is short and basically consists of climbing about 100 steps.
- Bullock Texas State History Museum - A good museum if you like history. It has an Imax theater, rotating exhibits, and a film on the history of Texas. There's also the LBJ presidential library on the campus of UT if that's your thing.
- Tour of the State Capitol
- Explore the University of Texas
- Catch the Congress Ave bat colony flying out from the bridge at dusk. Get there a bit early. I would recommend standing on the bridge above them as they fly out. It's the largest urban bat colony in the world and they put on a show every night.
- Catch a AAA baseball game in Round Rock at the Dell diamond. Across the street is Kalahari Resort, the largest indoor waterpark in America. It has a full suite of arcade games, rock climbing, laser tag, bowling, etc.
- If you've ever wanted to see what justifies an $8 donut, give Gourdough's original food trailer a try on South 1st Street.