For a short stay, it's got plenty to keep you occupied -- NASA, Museum District, shops at Galleria and Westheimer should keep anyone occupied. I stayed for three nights -- probably exactly the right amount.
Check out the Beer Can House, a home covered on the outside with decorative beer cans near Memorial Park; La Carafe bar on Market Square downtown; the student pub at Rice University known as Valhalla; El Pueblito restaurant on Richmond near Mandell; and these trendy coffeehouses: Diedrichs on Westheimer and on Montrose, Cafe Artise at West Main and Mandell, Cafe Brasil at Westheimer and Dunlavy, and Agora Cafe on Westheimer just west of Dunlavy.
Kemah is cool, but try taking the ferry from Galveston to Bolivar Island. The beaches are quieter and you can see dolphins sometimes on the ride over.
Be sure to visit Kemah -- off Highway 146 midway between Galveston and Houston -- for great on-the-water dining and peoplewatching. If you love boating, you'll love the parade of boats of all kinds heading out into the bay.
Be prepared to have your deodorant handy! Walking around Houston in the summer is like being in a steamroom. I've never perspired so much in my entire life!
Definitely go to the Space Center. Eat at Butera's in the museum district. The aquarium has amazing atmosphere - and a great restaurant, but I've seen better fish.
I think Houston is a great city. It may not be the most exciting place to visit, but hell that doesn't matter. It's one of the greatest cities in the world.
Although you have limited choices when it comes to hostels in Houston, it is the largest city in Texas, Houston is home to about 2.3 million people in the city area and almost 6 million in the whole metropolitan, making it the fourth largest city in all of USA. Houston is particularly known for it's Space Center ("Houston, we have a problem"), and it's museums. The city was founded in 1837.
The city is served by it's own airport and bus / train operators (Amtrak for one). When moving inside the city, bear in mind that Houston covers a massive land area, and you need to utilize some kind of transport to get to and from your Houston hostel, be it public (which is just the city Metro) or your own car / rental. Having your own transport is a great advantage in Houston (and in USA generally), so you should seriously consider it, especially if you're not traveling alone which makes it great value too.
Houston hostels are mainly concentrated on the main city area. The rooms are generally good value and the hostel staff can be of great help when arranging your daily activities.
The main thing to do in Houston is of course the Space Center. Situated in Clear Lake, the place is great fun and you should spare at least half a day to explore all the activities they offer. There are also plenty of museums in Houston (Museum of Fine Arts, Childrens' Museum, the Houston Holocaust Museum and so forth).