Halfway would be somewhere between Dallas and Houston. Not much there of note....
The best I can think of that would be convenient is Huntsville State Park in Hunstsville, Texas right on I-45 about 130-140 miles from Galveston. Any closer and you would be in Houston. Any further away you would be in Dallas. There are other nice places close to Dallas but none as close to the I-45 corridor. Its a state park and has a nice lake for fishing, boating and swimming. Check out the following website for more information:
http://www.tpwd.state.tx.us/spdest/findadest/parks/huntsville/
Howard in Houston, Texas