The Florida State Parks has some excellent parks on the Gulf. St Andrew's, St George and St Joseph's Peninsula SP for a start. Those are more or less south of Tallahassee. Florida Caverns and Three Rivers are near the GA border I believe. Eglin AF Base may have something but I haven't heard of it. Three Rivers would be fishing friendly.
Check out this site:
MapOcklockonee SP is another park probably good for fishing. Most of the other parks east of Panama City (that I didn't mention) probably aren't suitable. You can check site sizes on the ReserveAmerica site.
I found this on Eglin but I'd guess it's way out of your 7 hour range:
EglinDepends on where you are in GA.