It's surprising how often this bare bones question is asked here. Since Houston is the 4th largest city in the US, it would be helpful to know your tastes and price expectations. All of the above are good suggestions, although I would research Oxheart before going there, it's not for everyone.
Feast - 10 minute drive from downtown, quite good "nose-to-tail" dishes https://sites.google.com/site/feasthouston/
Reef - good seafood, modern trendy vibe; also about 10 mins from downtown http://www.reefhouston.com/
Brennan's - upscale old-school Gulf Coast cuisine; haven't been there in years, used to be very good; expensive
Hugo's - Upscale mex-mex, have not been there but it gets lots of good reviews. http://hugosrestaurant.net/
Also check out b4-u-eat.com, you can search by neighborhood for reviews
That's a great list. (I love Brennan's.)
I would only add Uchi, the local expansion of the Austin-based, Beard Award-winning burgeoning empire:
El Real, the old school Tex-Mex Mecca owned and operated by a trio of local foodists:
They're within a block of each other, so if it were me, I'd do both, but I'm a P-I-G hog, (as Justin Wilson would say).
You need reservations at Uchi.
Enjoy your visit and please let us know what you do, (did) and how you found it.