There are some sunken ships just offshore within the area. You could probably find a tour to one (though, I don't know how deep they are). If you have a SCUBA license, that will help with the wrecks and artificial reefs.
There is a Gulfarium somewhere along the island (I think near Navarre, possibly near Destin).
Go to McGuire's Irish Pub. Go to the Beach if you're into that. If you're willing to drive there's plenty to do along the island all the way into Alabama (Orange Beach, Florabama, Gulf Shores, Gulf Breeze, Pensacola.) Some of the local State Parks can be serene if you just want to get a breather and relax. Definitely get in contact with any of the local Airmen. Those dudes will know the hot spots to hang out. There's a bar somewhere in Destin(?) where you can do Beer Tastings and have dinner, I think on Tuesdays.
When I was stationed at NAS Pensacola I frequently saw some of my buds from Hurlburt hanging out at Seville Quarter in Pensacola. It's not a great spot, but it's known in the area. Also, NAS Pensacola itself is pretty cool. The Navy Air Museum is worth it. I never went to the lighthouse, but heard good things.
Also, there's an armory (armament?) museum on Eglin.