I haven't been to Galveston Island State park since they did renovations after the last storm, so I have no current information. They have sites on the beach and sites on the bay.
We actually like the county park Dellanera RV park which is on the beach (well, behind the dunes) and has full hookups. https://www.galveston.com/lodging/rvpark/dellanera/
You might want to check out High Island which is just north of Galveston. Sea Rim State Park is there, but they only have electric and primitive sites.
That island was pretty much destroyed by a storm (forget which one), so the areas where homes once stood have been developed into rv parks. I haven't been there personally, but a friend has been and said the parks are nice. https://campgrounds.rvlife.com/regio...as/high-island