Houston is the 4th largest city in the USA. As such it has many, many attractions and tourist destinations.
Houston is second only to New York for the number of theatre seats, and has permanent resident companies for opera, symphony, ballet and theatre. See this page for more information.
Houston also boasts thousands of restaurants. Given the city's broad ethnic diversity, it's safe to say there isn't a cuisine that isn't available here. It would be impossible to list all of the wonderful restaurants that a visitor should try, but at a minimum you should try a steak restaurant and Tex-Mex. Yelp is a great resource for finding the best cuisine in Houston.
No trip to Houston is complete without a visit to NASA. The Johnson Space Center as it is officially known, is home to Mission Control and the training facility for the International Space Station.
There are professional teams for all of the popular sports in the USA, including basketball, American football, baseball and football (soccer). For the week of our wedding, the Houston Dynamo will be playing Montreal and Sporting KC at home. The Houston Texans will be away that weekend, but they will be hosting the St Louis Rams the following Sunday.
Many international music acts visit Houston when on tour. The Houston Press lists many of the gigs in town, large and small.
If you want to get away to the beach, Houston has a few options, although do note that this part of the Gulf of Mexico is not the bluest due to the Mississippi River outflow. Galveston is an old port city that at one time was larger than Houston. Directly South of Houston is Surfside which is a little more peaceful. If you're looking for white, sandy beaches, Corpus Christi and South Padre Island are a good bet, but are about a 4 hour drive away.