Not sure if you want to come this far east, but Carrabelle (20 miles east of Apalach) is a great place to keep a boat.* We are at C-quarters marina, wet slip is $300 a month, including water and power (50a or 30a).* Slips are deep, the river offers good protection against all typical winter weather.* I'm down at my boat about 3 or 4 days a week, I'd be happy to keep an eye on yours as well.*
The moorings is also in Carrabelle, better known and more money, they offer cable tv, but they are about $60 a month more.
Carrabelle has all you would likely need, a good, clean grocery store, a small and expensive marine store, library with internet access, A haulout facility, decent restaurants, all within easy walking distance.
Marine Systems is a full service diesel shop, they do good work and are right on the docks at c-quarters.
Tallahassee is 50 miles away, where there is a good airport.
Panama City also has a number of good marinas, we liked Sun Harbor when we passed through this Spring, it is inexspensive, and has fair slips.* Nice people, not great protection.* There is a small airport in PC, or you can drive to Tally, which is about 2.5 hours.* There are other marinas in PC as well.
Destin/Fort Walton are most likely going to be more expensive as they are more "resort" oriented.
Can't say too much about Pensacola, though there are a number of good Marinas there, and an airport.* Probably you could find something there for less than the Destin area.
Are you staging for a trip south?