I've only actually camped "on" the beach with a tent, but in the last month I've camped at state parks that were "next to" the beach. St George Island in FL, Goose island state park in TX, and Galveston Island state park in TX.
Goose Island we actually had the water right out the back window of our Scamp
, but there's a seawall there so it's not really "beach". We liked Goose Island. Galveston Island state park had some sites destroyed by hurricane Ike, so the closest sites are just behind the sand dunes, and have electric and water, plus a shelter with table. Another nice campground.
As we departed Galveston and went through the Bolivar peninsula in TX, it appears that there are several areas that you can just pull onto the sand and camp, so you might check into that.
We would have spent a night or two on Padre Island National seashore, they have sites on the beach there and also at Mustang Island state park, but thunderstorm predictions hastened our side trip to San Antonio instead.