Well the wife and I have been to the Cape San Blas area several times, but honestly I don't recall ever eating in the area. Except for an ice cream cone once or twice. Nothing comes to mind trying to remember a eatery around there either. Seems to me there was a burger joint near Indian Pass a while back, but I think it was closed down last time we drove by it. There may be a restaurant up on the peninsula of Indian Pass, but I'm not really sure. Seem to recall seeing signs but haven't actually been there to try it out.
In Apalachicola, there are a few restaurants, but nothing spectacular as far as quality is concerned. We sometimes eat at Papa Joe's at Scipio Creek, and the fried shrimp, at least, are decent.
Connie and I have talked about renting cabins right in the state park at Cape San Blas for years now, but never gotten around to doing it. If you haven't checked that out, you probably should. Pretty remote and the cabins look pretty nice.
Sorry I can't be of more help....
Oh, btw, on the way out there, you will probably go by a place called Angelo's near the Ochlokonee bay bridge on route 98. Nearly everyone who has eaten there has said they will NOT go back. So bear that in mind if you see it and think about stopping in.