Let's see...if you were to visit me in Houston...we would have so much to do and see:
For starters, we could hop on the Metro

and visit the Museum District, which has eighteen museums for us to check out.
If you're looking to spend some time outdoors, we could visit the Armand Bayou Nature Center, where we could take a guided tour or a canoe or pontoon boat ride to check out over 370 species of birds, mammals, reptiles, and amphibians. ABNC is the largest urban wildlife refuge in the United States.
After viewing all of the gators

while on the bayou, we could head down to the Downtown Aquarium and sample some fried gators for dinner.

. The Downtown Aquarium is a 500,000-gallon under-water adventure complex which includes a Ferris wheel, an aquatic carousel, Shark Voyage, a white tiger exhibit and a restaurant. They have great seafood and the views of the aquarium are fantastic!
One night, we could head down to The Theater District downtown, where we could catch a show at one of the eleven theaters/venues.
If you want to spend the day shopping, we could go to Galleria

and shop at over 375 stores, eat at one of the 30 restaurants and then take a few laps around the ice rink.
If it's bargains you want, we could ditch the high end department stores and specialty stores at the Galleria and head over to the Harwin Drive Shopping District

. It's bargain shopping at it's best!
On the way back home, we could stop at the Glenwood Cemetary and check out Howard Hughes' grave site

. People always want to see where old Howard was buried.
We could go down to NASA's Johnson Space Center

and check out all the cool exhibits they have for the public.
That's just for your first trip down...there is so much more to see here in Houston!