After Labor Day I would suggest St George Island. You can camp at the state park and rent kayaks and fish the bay or surf fish the Gulf. Your son will love it and it’s affordable. Even if you decide to stay in a hotel in Apalachicola or Eastpoint instead of camping. Even the Buccaneer Inn on the island will have cheaper rates in the off season. Let me know if I can help on some good spots.
I thought we weren't allowed to speak of the best place on earth for beach stuff.

The fishing is hit or miss there - my favorite place on the coast - some days the 7 pound trout jump in the cooler and some days there are no bites. If just going to the beach to fish - hit Peach up and go to Navvare pier.