Southern Texas has several state parks and national seashore that offer beach camping. I have visited and camped on Crystal Beach, Bolivar Beach, Galveston Island, Surfside, Freeport, Mustang Island, North and South Padre. All offer a little slice of heaven in my opinion. I have not checked out Matagorda but hopefully will get there this year.
The area offers both free and paid beach camping. The paid camping areas usually have a yearly cost of $10 or $15 USD for a whole year, so very minimal cost even for a few weeks. The free spots are usually a bit more remote without any services or grocery stores nearby.
I found cell reception varied from beach to beach. I do some remote work and use my phone hotspot, so good cell reception is one of vanlife my must haves. Having a cell booster may make my life easier and I am considering purchasing one at some point.