Oh, the possibilities are practically endless.
I definitely second Petunia's suggestions of Cuzzins and Gladys'. Great local food like roti ( my favorite ) as well as more exotic dishes such as goat and oxtail, but you can get a chicken sandwich or hamburger, too.
Iggie's is also fun and right on the water. And plenty of room to move around.
How about here:
St. Thomas Skyride to Paradise Point - Ride The View - Home
Your tour will probably take you here anyway. If you click the To Do button you'll see a link to dining. There are lots of cruise ship passengers who go up there because it's right across the street from the dock. And up a mountain. You can take a tram (there's a charge) or you can drive up there.
Tickles is also close to your price range and it's on the water in Crown Bay, but there isn't a beach. It's in a marina and there are usually quite a few locals hanging around. They don't have their own website, but this is from a blog:
Tickles Dockside Pub - Winner of Best of St. Thomas 2008 Award
Hook Line and Sinker in Frenchtown may be a good choice for you as well. A warning though. In September it can be oppressively hot in there. If there's a breeze, it's great. The last time I was there which was about 2 years ago there was no a/c. It's right on the harbor in Charlotte Amalie and you can watch the seaplanes take off and land.
Hook Line & Sinker, Seafood Restaurant - Frenchtown St. Thomas, Virgin Islands Caribbean
If you want to go to Red Hook on the east end of the island then maybe Duffy's Love Shack. I think every visitor to the island winds up there at least once:
Welcome to the Islands!
Or if you're really serious to sticking to $15 p.p. then try Burrito Bay Deli. It's across the street from Duffy's in American Yacht Harbor. There's no table service. It's a counter where you order and you grab your own drink. There are actually very few tables inside, but there's a long counter outside where you can sit and there's also a few picnic tables between the building and the docks. I used to have breakfast there almost every morning when I dropped off the FH for work. It's, in my opinion, the best value for your money on the island, but there are absolutely no frills. It's deli paper and plastic cutlery. You can order ahead and have the food waiting for you. They don't have a website either but this will give you a good idea and a link to their menu. It's over a year old, but I doubt much has changed:
St. Thomas Restaurants, Bars, St Croix Restaurants, St John Restaurants, Virgin Islands Restaurants and Bars, Dining out St Thomas, St John Dining out, St Croix Dining out, Restaurant guide for St Thomas
Sorry if this is overwhelming, but during my time of living on St Thomas I obviously ate out more often than I cooked.
Re: St. Thomas after wedding plans? 
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