There are so many! Depending on which side of Houston you'll be on....
Space Center Houston
Clear Lake area recreation parks
Kemah Boardwalk (restaurants, amusement rides, and boat trips)
Galveston Island
Moody Gardens (on Galv. isle)
Gulf Greyhound Race park (greyhound races)
San Jacinto Monument
US Battleship Texas, Battleship Park
Galleria (shopping, ice skating)
Richmond Avenue (tons of night clubs)
Museum District (LOTS of great museums)
Theatre District
Houston Zoo
Miller Outdoor Theatre
Sam Houston Race Park (horce racing)
SplashTown USA
Houston has so many different types of things to do...have fun!