It's too bad you "don't do state parks" (wth does that even mean??) because a quick google search will show that you can tent camp at the beach at Galveston state park.
Best of luck to you... Was only trying to help...
Galveston Island State Park Campsites
Campsites with Water and Electricity (Premium - Beach Side)
People per Site: 8
Number of Sites: 36
Weekly and monthly rates are available from November - February. These sites are suitable for tents and RV's. Sites have a shade shelter, picnic table and ground fire ring. Restrooms and showers available only in first and third loops. Only two vehicles allowed per site. An RV or trailer counts as one vehicle. All sites are back in sites.
30 amp hookup
50 amp hookup
$150 Weekly Non-peak
$625 Monthly Non-peak