-Houston Aquarium: it's in Downtown Houston.
-POST Houston: It's a Food Hall featuring local restaurants and has an amazing Sky Lawn with a killer view of Houston's skyline. Probably only good for an hour or so though. Not much to do besides get food and check out the view.
-Hermann Park: one of the best parks in Houston. Great place to walk around. Lake has pedal boats!
-Houston Zoo: Right next to Hermann Park.
-Museum of Fine Arts: one of many great museums in the Museum District. Short bus ride from Downtown area.
-Space Center: fun place to explore for any age, and they have a food court as well.