I know some people love AI, but usually "all-inclusive" and "good food" don't go together. Exceptions are places like Palm Island and Peter Island, where the resort is the only thing on the island. It is also hard to find a luxury, adults-only hotel. Look at Cap Juluca in Anguilla. It is more private than Viceroy, and IMO on a nicer beach. Consider a week at Palm Island and a week in Mustique. Also, you are less likely to find children around if the honeymoon is not during a scheduled school vacation

Four Seasons, Nevis is NOT an All Inclusive Resort. It's also quite popular with families suit won't meet your definition of Adults Only.

Agree with beachykeen - on Anguilla check out Cap Juluca - The room rates include breakfast and you can purchase an optional dinner plan but Anguilla has over 80 different restaurants on the island (some among the best in the Caribbean). You'd be doing yourself a disservice limiting your meals to just the resort.

Skip La Samanna - that place has been resting on its laurels for years.

Peter Island is a perfect honeymoon location but if you are interested in the BVI's also look at Little Dix Bay on Virgin Gorda.

Skip Sandals on Antigua - it is simply not in the same class with some of the other resorts on your list.

Galley Bay is a nice resort but a step down from Cap Juluca, Four seasons , Peter Island and Little Dix Bay.

Haven't been to Palm Island so I can comment other than it's a little difficult to get to.

I've been to Palm Island. I would go there in a heartbeat...and since you will be on your honeymoon- how romantic...and the back story on Palm Island is so romantic - read Desperate Voyage by John Caldwell. You can make daily trips to Union Island - provided by the resort....I'd go there in a heartbeat.....

Another thought....to get to Palm Island, you fly to Barbados and then you are met to fly to Union Island. Perhaps consider hanging in Barbados for a few days and then go to Union Island....

palm island also offers day trips to http://tobagocays.org/ arguably the best snorkeling in the caribbean. friends have stayed & thought it was wonderful.

They will look after you at The Viceroy in Anguilla. Lovely country, excellent hotel and really friendly people; I can't recommend highly enough.

Palm Island is my favorite place in the Caribbean. You usually fly into Barbados (depending on where our depart from)and the following day, you fly into Union Island and then take a 10 minute boat ride over to Palm Island. At the end of your vacation, they take you back to PI, and you fly back to Barbados to take your flight home. You could spend some time in Barbados ahead of time and then eventually head to PI. At the point of hitting PI, you will be greeted dockside with a rum punch, fall in love with the staff and enjoy many great meals. In the winter, kids are not allowed. Make sure you go to the Tobago Cays with Yannis whether you snorkel or not. The ride, lunch and the rum punch alone are worth it. We've done it on each of our three trips there and my husband does not snorkel.
Sandals Antigua would not be on my original list. Too many people for a honeymoon and the only decent food is the pizza.
Jumby Bay is very nice and has clear blue water but the seaweed keeps it far from being a perfect beach.
Four Seasons Nevis is very well run with an incredible staff, fun monkeys and you can take the ferry to St Kitts for a nice day trip. Not an AI, although many people never leave the resort as they are so happy there. I expect you would want to have dinners out as there are many wonderful restaurants around and the dining is an experience! We expected kids, but there was only one and we only saw him once.

It does seem like AL resorts have so-so food. I'm going to end up doing AL, but with your budget I would just look at menus at the places you're looking at and take that out of your budget and pick the room accordingly.

With this budget, you should definitely browse Amanyara in turks and Caicos. I'm not sure if its AL, but I doubt many families would go there because it rated to be very romantic.

With this budget, why not look at St Barts? Maybe not for 2 weeks though, but split it with somewhere else. It's the French Riviera in the tropics and you can't go wrong with the food.
I was not keen on the location of Sandals Antigua, it was on a busy stretch of beach and the surrounding area not very pretty.