Pat's is still around. Good if you want fried stuff and diner food.
Agree with previous suggestions, I'll add a few:
Pizza: Callahans is awesome for pizza and pizza rolls. It's a bar downtown, not sure how old your daughter is. Bootlegger's is also good and downtown, too.
Seafood: McAdoo's. Also downtown. Pretty good eats. It has a knockoff out on the Loop called The Reel, which is also very good but not as good an atmosphere.
Steak: Myron's, also downtown. It's a little drive, but Kindling in Cibolo is excellent, too.
American food: Huisache Grill, also downtown. There's another place called Texas Bistro that is really good, too.
Burgers: Agree on Tin Top. Some people really like Muck N Fuss, and the atmosphere is awesome there. I prefer the Tin Top burgers, though
Mexican: Plenty of choices here but for an out-of-towner I'd recommend La Cosecha. Good atmosphere and some of the menu items are excellent (wagyu fajitas, some of the specials)