http://en.wikipedia.org/wiki/St._George_Island_%28Florida%29
My wife and I got married in one of the houses. The structure in the photos is actually a pavilion in the state park at the northern end, but there are a number of houses for rent, and some condos, both on the beach and further inland. There is even a bed and breakfast or two. Rentals right on the beach tend to be more expensive, but access isn't usually a problem except that the dunes and the sea oats are protected - obey the signs or you face fines.
If the tourist industry has recovered from the BP spill yet, you'll want to book your reservation ahead of time, especially during peak season. The best beach is on the Gulf side (east) and most of the fishing dock houses are on the bay (west) side. The restaurants and bars are pretty good, though maybe a little pricey at times, but the best seafood you don't catch yourself is from one of two competing panel trucks, Dail's or Doug's. Their stuff was usually caught that morning and they're both nice enough people.
If you stay more than a day or two, consider the short drive to Apalachicola back on the mainland. There are a number of stores and restaurants there. My favorite is the Apalachicola Seafood Grill -
http://www.yelp.com/biz/apalachicola-seafood-grill-and-steaks-apalachicola - the grouper is supposedly one of their specialties, but I had a cheeseburger there that ranked in my top three lifetime best.
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