WHAT TO DO
Since you are in Texas, you could go to the Houston Livestock Show & Rodeo , which is the largest rodeo in the world. Concerts, rodeo events and a carnival should keep you busy for couple of hours.
There are also several festivals hosted by the city, including Houston Children's Festival, the largest celebration for children in the US and WorldFest-Houston Film Festival (which already has a tradition of over 40 years).
Several museums might attract your interest as well and if you want to burn off some calories after trying the city's restaurants, there were some parks in the city.
George Bush Intercontinental Airport (IAH) is the second largest airport in the state of Texas and receives plenty of flights to Houston, including international ones. The airport is located just 23 miles north of the city. If you plan to drive to the airport, you can book Houston airport parking in advance and save yourself some time and money. Another very good option is to book a Houston airport shuttle in advance which will also save you from a lot of headaches and will give you a save ride from home to the airport and back.
WHERE TO STAY
The largest city in Texas can be a bit misleading when it comes to booking Houston hotels. Just because it is so big, you can end up booking a hotel miles away from downtown and then your "deal" doesn't sound that good, does it? With a little planning though, you can find good hotels uptown. Also, there's always the possibility to stay at a Houston Hostel.