I second Bruno's. Worth the drive. If you must stay in Panama City proper, go down to St. Andrew's to a place called Enzo's. And get the double decker.
If you guys are coming over to 30A, try Pickle Factory in Grayton Beach. How about Panama Pizzaria on Front Beach Road? I haven't been in a few years but I recall it being pretty good.
There is a joint near the Summit that we went to last time called 3 brothers from Italy. I don't know if I was starving or it really was that good but we destroyed a pie. It's NY style. I'll find out again when we go back this summer.