We just stayed for 3 nights at Brazos Bend State Park in Needville Tx outside of Houston at the begining of February. It's probably an hour to downtown, might work depending on where in Houston you are going. It took us a half hour to get to Sugarland in rush hour.
The campground has nice bathrooms, laundry, really big campsites. We stayed in the 200 loop under a HUGE live Oak. $20 a night with electric and water but you also have to pay the $7 per day entrance fee. Overflow lot was pretty nice and was $12 per night. The annual pass for texas state parks was expensive at $70.We saw a lot of birds and 21 alligators when we walked around Elm lake. You definately need a reservation for the weekend, we didn't need a reservation for the weeknights. When you reserve, you dont get to pick a spot until you get to the campground.