Tex Mex - El Tiempo (best fajitas on the planet IMO), the original Ninfas, or Guadalajara
Fast Tex Mex - Fajitas A Go Go
BBQ - Killens, Truth, Pit Room, or Blood Brothers
Burgers - Bubbas Burger Shack (it's under a bridge)
Breakfast - Egghaus, Harrys (diner), also it's a chain, but Black Bear Diner.
Cheese steak - Papa Gino's
Italian - Prima Pasta
If you only go to one of these places, make it El Tiempo.
Perrys is good but it's a chain. If you go, get the pork chop.
Rice Village has gotten more upscale and corporate. A lot of higher end chain bars and restaurants are there now, if that's your vibe. But Little Woodrow's is still there...
I want to also recommend my favorite brewery in the world Buffalo Bayou, but sadly it's closed right now.