You definitely want to go on the Texas State Parks website to find the status of the places you're interested in. The PINS park, as mentioned, is primitive and first come, first serve; but there is a welcome center nearby with a little store for the basics. A dump station is also available. The beach is very nice and the road to get there is finally finished with construction.
Mustang Island and Goose Island State Parks are two of my favorites. They have power and water and are well run, but currently closed due to the hurricane.
Here's some links:
Padre Island Nat. Seashore -
https://www.nps.gov/pais/index.htm
Texas State Parks Alerts -
https://tpwd.texas.gov/state-parks/p...k-alert-status