Lynnandcarol's routs are the way to go. When you cross into Texas stop at the Texas Visitor Information Center, exit right just after you cross the Sabine River(state line). Pick up free Texas maps and information guides and camping information. Plenty of room to park your rig.
When you get to Winnie exit I10 onto state hwy 124, past High Island you will turn right at the dead end onto state hwy 87 to the Boliver ferry just past Crystal Beach. When you get into the ferry line , get out and turn off your propane. The ferry is free and plenty of room for your rig.
There are 2 ways to get out of Galveston, north on I45 to state hwy 6 to Alvin and left on state hwy 35 to Rockport, or FM 3005(Galveston Island beach road) west thru Jamaca Beach to Surfside Beach. There is a toll bridge to get across San Luis Pass and off of the Island, $2.00. Right on state hwy 332 across the GICW bridge, left on 523 at the light thru Freeport to state hwy 36, right to state hwy 35 and left to Rockport.
All the state hwys are good and safe with great views and lots of small town Texas charm. Enjoy the trip.
The roads are good, wide shoulders. I get confused about which lane to be in for the turn in Jourdanton so watch the road signs carefully. You have to watch out for small town South Texas traffic, they have the right of way( they think.)
Have a safe trip,
You may want to try Padre Island National Seashore. Not quite to the valley but still warm and great beach camping. Fresh water available and a limited supply of food in the visitor center store.
You can camp on the beach in Port Aransas on Mustang Island for 3 nights for $12. beach parking permit. Lots to do and see in Port A.
When you enter Texas stop at a visitor center and pick up a camping guide. Move off of the interstate to Texas state highway 35 as soon as possible. It follows the Gulf from Houston to Corpus Christi with plenty of camp sites on the water.