Oasis on Lake Travis for drinks at sunset, food is OK but nothing to brag about. Some of my favorite places to eat in Austin are County Line BBQ on the Lake, Iron Works, Pok-E-Jos, Chuy's, Serrano's, Threadgills and The Tavern (very cold beer!).
In Austin here are some things to do, Climb Mt Bonnell, swim at Barton Springs, visit the Capital, visit Bob Bullock Museum, have a drink at The Driskell, check out the Continental Club, Antones (if it's still open?), take pictures with the Stevie Ray Vaughn statue on Lake Austin and with Willie's statue at ACL.
I don't know much about San Antonio but I do know to there's some very good Mexican food at the oldest family own restaurant at Jacala's at 606 West Ave. Of course visit the Riverwalk and you must stop at Dirty Nelly's and Dick's Last Resort. The Riverwalk has a County Line BBQ but I've always favored the one at The Lake.
Hope all this helps and welcome to Texas amigo!