You need to have breakfast tacos at Taco Shack (various locations- Google it.)
You need to have migas (also breakfast) at Bodega Vallarta at the intersection of South Congress and William Cannon (best if you can speak Spanish, but you can get by with English.)
The museum scene here is okay but not jawdropping- walking around the UT campus is more fun. And if you do drop by campus, check out West Campus (just to the west of Campus
) and you will see all the redevelopment we have been talking about here. Campus here is an electric place- really worth the time if you want to wander about a bit.
If you like greasy burgers and milkshakes- check out Players on MLK right by campus.
For finer dining, Chez Nous (traditional country French cuisine) or Mirabelle (more continental and elegant) are must tastes- very unique in the grand scheme of fine dining in the US.
There are lots of local walks and pools that are great to see- but I am not mentioning them because we have had so much freaking rain that most of them are closed right now.
Austin Wine Merchant on 6th street for great wines (Chez Nous and Mirabelle have BYOB as do most top restaurants here.)
Outdoor art festival every weekend at 6th near West right across the street from Katz's Deli.
That is about it off the top of my head. You are off-season for the various festivals and the rain has forced closure of most public recreation areas- but the great food and campus offer some good times.