I was there two weeks ago and within an hour of landing we were eating a sausage and cheese tray while downing Shiner Bocks at Schilo's Deli (
http://www.schilos.com). If you haven't been to Schilo's. it is a German Deli less than half a block from the Riverwalk that dates back to aruond 1920. Definitely worth a visit just for the hot mustard, but beware.
If you want touristy at the Riverwalk, we had a great blackened prime rib and prickly pear margaritas at Boudtros.
Also, we found Rosarios in Southtown which was great. Nice upsacle casual atmosphere, with a fantastic chorizo/mushroom cheese dish. When I go back I'll probably head here first. If you haven't been to Southtown, there is a very nice brewery, Blue Star Brewery, in the Blue Star Arts Complex where you can get a good beer and then rent bicycles to rider to the missions. (Maybe you should do that in the opposite order.)
Finally in Southtown, even though we didn't get there, Acuza was getting rave reviews locally as the place to go.
Have a good trip.