Went to this local little ice cream shop. Their ice cream base is GF so as long as you don't choose a flavor with cookies or cake or any other gluten item as an ingredient you should be safe. I had the creme brûlée and black cherry flavors.
Homemade ice cream with rotating flavors, sometimes daily. They have many flavors that are gluten free and all you need to do is ask about them. Dairy free options as well. We visited many times while we were Galveston. Never a disappointment.