You can forget it anywhere immediate to Pensacola but, not far away...
The western end of Santa Rosa Island, just before you get to the National Seashore is an excellent place to fly. That is where the powered paragliders go also. It is one of the few places not blanketed by a five mile radius. There are a couple of pullouts with beach access there also.
Otherwise it is a maze of airports, National Seashore, and Military Operations Areas, and unless you are p107 and know your airspace very well you'll spend a lot of your time calling airports.
Navarre is one other exception, with only a couple of airport notifications needed, and is on the other end of the National Seashore going east on Santa Rosa Island.
Also beware of numerous helos and military aircraft low over the beach area.