Big thing I'm looking for would be peace and quiet. Fewer kids is nice, no kids is real nice. I'd like warm sand, clear water, and moderate waves, say 4' max. Probably the best I can say would be something like Rehoboth with clearer water, fewer people, less noise, and just generally chill. Don't need a party place, don't need neon, don't need casinos. Just somewhere to detox from the tech that I'm immersed in 24/7.
If you really really want to get away from it all, Bequia (one of the Grenadines) is probably a good bet. English speaking, quiet beaches, friendly folks, and a local 169 proof rum that goes down very easily in a rum punch and will kill you if you have more than two. I like the Friendship Bay area personally but it's hard to go wrong anywhere there. Usually you fly into Barbados then take a small plane to Bequia - if you're not a steady flyer, you may not be happy in a 8-10 passenger propeller plane. St. Barth is also quiet, with amazing beaches - you could go to a different beach almost every day of the week. It's a small island, so it's never more than a 20 minute drive to get anywhere. It's so small that a few years ago my hubby was actually able to circumnavigate it on a jet ski. It's frequented by the super rich, who apparently never go to the beach, because the beaches are uncrowded, even in high season. It's best that you have some basic French, and it is pricey, but if you are willing to go in low season, you can rent a small private villa at a reasonable rate. Our favorite is Villa Sud Ouest:
http://stbarth.com/villas/detail/sudou/sud-ouest. Private villa with pool for $1670 a week in low season. Getting to St. Barth is by way of St. Maarten then you either take the ferry or a 10 minute famously hair-raising flight in a very small plane to get there.
Larger islands are more populated, but are a lot easier to get to in a normal size plane. With a little searching you can find some quiet nooks where cruise ship tourists tend not to go. St. Kitts is nice, English-speaking, with pretty beaches complete with beach shack bars, an extinct volcano for hiking, a World Heritage Site fort, and even the gravesite of Samuel Jefferson, whose g-g-g-grandson was some guy named Thomas Jefferson. The Timothy Beach Resort is a low-key condo place - not luxurious, but you get can full apartments with a separate bedroom and full kitchen at a reasonable price. If you're going in high season, check the cruise ship schedule - if there are two large ships there on the same day, they tend to overwhelm some of the more popular tourist sites, so that's a day to stay at your hotel and enjoy the pool or nearest beach. St. Maarten is also nice with some lovely beaches. And as mentioned before, St. Lucia is a bit larger, but relaxing, especially at some of the smaller bays and beaches. But it is large, so if you want to see different sites on the island, then plan on either renting a car, shelling out a fortune for taxis, or braving the local jitney buses.
Whatever you do, I would highly recommend that you rent a place with a kitchen or at least a kitchenette. Even if you go out to dinner most nights, having a place where you can make coffee and your own breakfast in the morning, then come in from the beach and make a few sandwiches and a cold beer for lunch will save you a fortune.
Also, about Key West - I agree completely that it's anything but quiet - sorry I wasn't clear in my post about that. But it is fun for a day or two, but agree that the Middle Keys are a much better bet for quiet.
You're making me want to plan my next trip to the islands!