It really isn't all that great, Fungs is the best chinese in the city hands down, Carrabas is good as long as you go to either the one on Voss or Kirby as they are the only 2 still owned by Johnny, others are franchised out and are hit or miss. For Italian we generally go to Carrabas (pollo rosa maria is incredible), Maggiano's ( a highschool friend of mine is the bar manager there so free drinks) or La Grilga ( this is walking distance from my house)
You should eat some seafood since we are right on the gulf, Pappadeaux Seafood Kitchen part of the Pappas family which originated in Houston or Ragin Cajun Seafood. Those are in Houston if you venture down to Kemah or Galveston there are too many good seafood places to name.
I'll be honest I'm not a huge seafood person unless its sushi so there could very well be better places then this.
BBQ - strange as it seems Houston really doesn't have an outstanding BBQ place when compared to other Texas cities. My favorites in order would be Luling City Market, Thelma's followed by Goode Company.
and Tex- Mex only 2 places you need to know El Tiempo Cantina and Lupe Tortilla's, Lupes is known for their fajitas and margaritas.
Being Texas we have several outstanding steak houses, Pappas Bros, The Strip House, Perry's Steakhouse & Grille, Vic and Anthonys, The Capital Grille and Sullivan's Steakhouse to name a few. All of these places are top notch and will cost some $$$ but well worth it.
If there is an Astros game while you are here go, the stadium is great and you can get tickets relatively cheap for mid week games, if the weather is nice they open the roof and the downtown skyline is the back drop.