Blythe Island Regional Park & Campground in Brunswick, GA is $500 per month + taxes. It's a county run campground, but it has full hook-ups, cable & free WiFi. Lots of trees, so satellite tv probably won't get signal unless you are along the lake. Lots of trees means lots of shade and that would be a good thing in June, July and August in Coastal GA. It's a little over 4 hours at the speed limit w/o traffic to Tampa, just about 275 miles.
Coastal GA RV Resort, also in Brunswick, GA is $600/month + tax. This is a private campground also with full hook up, cable & WiFi. Small trees, so satellite tv wouldn't be a problem. No trees also means no shade. This is about 4 miles closer to Tampa.
Both campgrounds are off exit 29 of I-95 in Brunswick, GA. 20 Minutes to Jekyll Island, almost 30 minutes to St. Simons Island. Just over an hour to Savannah, GA and just under an hour to Jacksonville, FL.
-Michael