Just got back from a 9 day trip. Primarily ate only local food but will share a bit of info:
For once, it's a good idea to eat in the airport! Great restaurant run by lovely Nevisian women - very affordable menu of local specialties. Had a great lobster club sandwich. Do not miss the sea moss. Even if you don't normally like this drink - their version is sublime with just the right mix of sweetened condensed milk.
At Phinney's beach. Gets a lot of Four Season customers who walk over. FABULOUS beach bar with friendly service. I had at least 3 meals here. They serve a wonderful mixed green (frisee in the Caribbean!?) salad with entrees. "Buffalo" wings were really just barbecued but quite good, falling off the bone tender. Ribs were better one day than another. Huge portion, lightly sauced, clearly not brined as the meat one day was tough. Local lobster is served with a garlic butter sauce. Grilled fish was my #1 favorite. An amazing mahi mahi that must have just come off the boat. Get the conch if they have it (often then don't). A bit pricey compared to other local food outlets, but you can't beat the location.
Key Bakery in town (One street over and around the corner from Superfoods - sorry I don't know the roads)
Friends get absolutely INSANELY CRAZY over their coconut tarts. Think empenada sized and shaped pie crust baked around a light, sweet grated coconut interior. I prefer the beef patties (they also have saltfish) - very different from the Jamaican style, more like empenadas but baked instead, filling wasn't very spicy and had some nice sweet/tangy seasoning going on - tomato or even perhaps a whisper of nutmeg or tamarind I wonder..?
High up on a hill overlooking the sea. You take a little trolley to get to the top. Great setting and view, food aims for upscale continental but isn't. Good, but not fine dining, offerings included ribs, some pasta, some curries and thai influenced dishes, a bit of everything. Ceasar salad with flying fish used boxed croutons - yikes! Entree of jerk pork wasn't jerk at all, but tasty enough. Served over garlic mashed potatoes that was probably a blend with sweet potatoes. Nice molten chocolate cake and good espresso. A destination for the view and good company.
Eddy's (in town)
One of the places more popular with tourists (though being a small island, there really aren't any "tourist traps" as compared to other destinations). Had a really GOOD fish and chips that was done with grouper. Huge meaty piece, very well seasoned. Friend had the flying fish - was at least 4 good sized pieces IIRC. Both served with fries. Great looking burgers here, too.
Most everything else I had in Nevis was local food from small places - two "food fairs" going on during Culturama (carnival) so I tried many different dishes (saltfish and johnny cakes, conch water, cookup, etc.). If you get the chance, try conki (or was it conchi?) - sweet potato with coconut, sugar, flour and spices wrapped in a banana leaf to cook. Think candied yams but way better. What you get looks like a tube of army green dough and darn is it good. I'm told it's often only made for special occasions like Christmas holiday. Also keep an eye out for truly homemade fruit punch. Wow.
In ST. KITTS
My one and only stop was Sprat Net about a 15 minute drive out of town. Go there. Go there now. Friends go twice a year and now I'm fiending for it, too. Built on a small cliff over the sea, it's an outdoor grill that does seafood and ribs, covered roof, picnic tables (like a New England clam shack). The ribs are fairly tender and flavorful. The lobster rocks - served spit open and grilled, covered in a garlic butter sauce. Comes with corn on the cob (boiled far too long) and 2 really light non-greasy johnnycakes. It is a tourist destination, but very popular with local folks as well. Get ribs as and app and get your own lobster and then go to town! Can't recall the price exactly, but was about $30 US for 3 lobsters, 1 order of ribs, 3 waters, 2 sodas and 1 beer. Well worth it!
There is a new shop across the street called Cake. Walk in and on display under glass are 4-5 cakes made fresh. Coconut cream won the competition - wow - but we also tried chocolate (very rich) and carrot cake ( a little bland). $4 US per slice or $10 EC (cheaper).