If you're not set on the coast, or have time to stop on the way there, the Double Lake Recreation Area in Coldspring Texas is worth a look. it is one of my favorites, surrounded by the Sam Houston National Forrest.
Big tall pines, lots of trails for hiking or mountain biking.
I like that on recreation.gov you can pick your exact spot. Some of the pull throughs have sewer hookups.
Huntsville State park is also another of my favorites.