Just a update since we just got back. We stayed a couple nights at the Allstar RV resort. Nice but kinda pricey for us.. not saying it's not worth it by all means. The rest of nights we were able to stay in the inlaws driveway. We didn't go Lakewood they said no parking and since we just got into town and was tired didn't try. Unfortunately after that my sister in law let us borrow her car for a couple days. 
The aquarium even though we took the car maybe on the RV parking if you went early enough. The museum of natural science which the zoo is also next door is a yes. The space center yes on parking just follow the bus signs. The kemah boardwalk yes but park further out so you don't have to pay. Didn't have alot of issues driving around Houston.