Few questions before I recommend places. Are you planning to drive to other cities? Also, which part of Houston are you gonna stay in? Below are my recommendations.
1. Brazos Bend State Park.
About 1 hour from Houston in driftwood texas. Very beautiful place. Usually on a sunny afternoon, if you are lucky, you can see alligator sunning itself on the trail. And if you are lucky, you can catch a glimpse of deers. I used to have annual pass to this park and go there once every other weekend.
2. Fossil Rim.
The largest safari style park near dallas. About 4 hour drive from houston... very nice place.
3. Enchanted Rock
off austin a very nice hiking place. Small little mountain to climb but scenery is priceless.
4. Big Ben National Park.
This one is about 8 hours away from Houston. But i can gurantee that the scenary is awesome.
5. Galverston State Park.
I call this place the sugei Buloh equalivent in texas... about 1 hour away from houston.. LOL
6. San Jacinto Battleship.
Dun really find this place interesting... but a lot of my friends like this place.. between houston and galverston...
If you still want to add more to the list PM me and I can tell you more especially if you wanna know what food is good and where to find it. I lived in that horrible city for 9 years... HAHAHHAHA