Check out
Henderson Beach in Destin. plenty to do like
St Andrews and not too far away.
Also Pensacola has a really cool campground
Big Lagoon, still easy access to activities.
St George Island is nice , but area activities are limited and you want to bring your own supplies.... Beach on both sides , but you would need at least a bicycle to reach them from the campgrounds.
Of course a little further west of Pensacola is fabulous
Gulf Shores in ALabama
Manatee Springs State Park in Chiefland is not really panhandle, but it is not too far south of it and is worth a look...