Good luck finding a cabin. It's all hotels and bed and breakfasts here now. Downtown has quite a few B&B if that is your thing, it is nice to be within walking distance of the bayfront/shopping/restaurants/historic sites. Although some of the prices are pretty steep, sometimes it pays to get a hotel on US1 since walking downtown is still only about 5 mins.
If you want beautiful sunrises, quiet private coquina beaches...and don't mind driving 5-10 minutes into town I'd say try to find a hotel on Vilano. North Beach camp resort may rent cabins (On Vilano) they offer beach access directly across the street, a jacuzzi, and there is a pretty decent seafood restaurant across the street called The Reef.
St. Augustine beach has the pier and is quite a bit more upbeat over Vilano, but you're limited to Chain hotels and touristy restaurants- there are several bars within walking distance though.
Restaurants to check out:
Caps On the Water - Better for Dinner. Great outdoor atmosphere, butts up right to the intercoastal with it's own pier and a pretty large tiki-bar. Great seafood all year round.
South Beach Grill- Better for Lunch. Delicious island food, homemade wraps, pasta salad, blackened shrimp, nom... Right on the beach, outdoor seating is best if it's warm enough, enclosed upstairs with panoramic views.
Creekside Dinery- right in town on US1, Better for Dinner- sitting right on the marsh, laid back staff, quality food, usually will have Live entertainment on Fri/Sat/Sun.