The best thing you can do in Houston is...... Leave!
If you get time, drive to Austin for the weekend. It's a lot more fun that Houston. It's a 2-1/2 to 3 hour drive, depending on where you are in Houston.
If you want some real local color, drive to Brenham and take the Blue Bell Ice Creamery tour. You even get free ice cream at the end! For added local color, drive about 20 minutes outside of Brenham to Greenvine. Go to The Green Door. It's an old country store/bar. Tell my Uncle Jerry that Leo sent you, and be sure to buy a t-shirt.
In Houston, it takes 1/2 hour to get everywhere. Really. I have scientifically proved it.
Johnson Space Center used to be a neat tour, but since 9/11/01 they've cut back a bit. Plus, the place was looking a little run down the last time I was there a couple of years ago, compared to when they first opened the new Disney-fied tour.
The Houston Natural Science Museum is neat, and they have a cool butterfly habitat.
Galveston is only an hour away, and they have a museum thingy there.
Houston has a few nice art galleries clustered together - the
Museum of Fine Arts and the
Contemporary Art Museum.
Check out the
Byzantine Chapel and the rest of the Menil collection.
There's always the
art car museum.
For an great grocery shopping experience, check out the HEB Central Market on Westheimer.
There's an old WW I dreadnought-style battleship - the Texas - about 1/2 hour from Downtown.
There's a little town near Clear Lake (NASA) called Kemah that has a little boardwalk-type thingy.
I'm sure others will have some ideas too.