Most of the hotels on the island require reservations for dinner and they stop serving after 9:00 pm. (Nevis is a relaxing Caribbean destination, and part of the plan for rest and relaxation is that you can enjoy your beauty sleep.) So not everywhere serves dinner late, but two of the late night dining choices on Nevis are of course room service at The Four Seasons or going to the smaller local restaurants.  (There are no drive-throughs or fast food places on the island.)  

On Nevis there are several high-quality, authentic Chinese Restaurants operated by people from Hong Kong. A quick plate of Won Tons is a delicious possibility for late-night food.

The small, truly local eating places on Nevis are completely used to having people drop in for music or socializing, and they will usually be able to fix up something good for you to eat on short notice.  Perhaps you could ask for fritters: they are fried and come with a dipping sauce. Chips (fries) are almost always available, and so is chicken.  Ribs from the Water Department (only on Fridays) or Mansa's are easy to find, and are quite exceptional.  Chevy's Calypso Bar & Grill (two minutes walk south of the Four Seasons Resort) will always be able to make you a sandwich at the very least. Sunday's are Reggae Nights with live music from 5pm and Mondays are great fun till late at Chevy's with Dinner & Karaoke fun! Rumours is also good for a late night snack.  Several of the local Rum Shops are open and sell fried fish and also chicken legs, you are safe and welcome there. (Have a drink while you are there as well as some food). 

Karaoke fun at Chevy's (that's Chevy, second from the right.)