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
Manatee Springs State Park
in Chiefland is not really panhandle, but it is not too far south of it and is worth a look...