Comments on what's been posted here.
Curacao is possibly a good option depending on flights from KC. It should be possible to be on the ground sometime around 2-3PM, it was for us flying in from Houston/Phoenix. Since we went in 07'
Insel Air has just started direct service from Miami 3-4 days/wk so it might be even easier now.
There's 5 AI's that I can immediately think of: Breezes in town, Lions Dive just east of there, Habitat and Sunset Waters west of town (about 20 mins.) and Lodge Kura Hulanda on the west end. I know nothing of Breezes, Lions Dive is a less expensive option, Habitat and Sunset Waters both were very tired looking. LKH is the nicest but no beach and it's a drive (45 min.) back to town. Were I on my honeymoon it would be the only one that I'd consider however due to the upscale niceness of the property.
Another option is the Marriott in Piscadera Bay, it's not the cheapest but it is probably the nicest hotel on Curacao. Right on the beach, a nice pool complex, diveshop on site and you can dive their reef just offshore. 1/2 hr. drive from some of the best Curacao shore diving and if you want something escorted, the DiveBus will pick you up there. 15 mins. to the airport also. We've recently been discussing Curacao options in some detail in
this thread so I won't repeat the details here.
My take on Virgin Gorda is that it's one of the places I'd consider for my honeymoon. Beautiful pristine beaches, in some places you're the only ones there, there's only like 15K people living there. It's one of those places where you don't lock doors at night, we didn't all week even though we were gone all day diving. Leverick Bay is one resort option, I think it's an AI also. DiveBVI has a shop onsite and theres something of a beach. It's very yacht oriented though - as is the whole island. Downside is that it's on the North side so a good 1/2 drive to town and most of the other attractions. They have the best beach bbq/party every Friday night, locals, tourists, everybody goes.
Little Dix Bay Resort is georgeous but pricey. It sits on it's own bay with good snorkeling. DiveBVI also picks up there. Every time we went in there to p/u divers, there were turtles diving for the bottom as the boat went by.
On VG you can snorkel the Baths, it's worth it. It's these massive boulders rising up out of the ocean. And
very private in some places (hint..

) Rent an SUV and there's several beaches on VG where you'd likely be the only ones around.
Downside of VG is the time it takes to get there. There's only a private plane sized airport and I don't know if they fly beyond Tortola. There's a regional airport on Tortola (Beef Island) but I think it closes down around September - at least it did 3 yrs. ago. But there is is really good fast ferry service between the islands so flying into St. Thomas early enough you might be able to get to/from either Tortola or VG the same day. Tortola is another option, it's a bigger island, has basically the same access to dive sites and there are AI's there. A couple in our party left VG on 8AM on the fast ferry and caught a 1PM flight out of St. Thomas.
We also went to Marina Cay one day. It's kind of a self-contained little island owned by the Pusser's rum chain. Although I don't think it's an AI. DiveBVI has a shop there and they have a nice beach and lagoon for snorkeling also.
http://www.pussers.com/outposts/marina_cay
St. John, is easy to get to also. Fly into St. Thomas, take a cab/shared van to Red Hook and there's multiple ferry options for the 20min. ride over. You can also catch a ferry downtown afaik. We were just briefly there but it seemed really quiet. There are some nice resorts there don't know if they're AI.
Even St. Thomas isn't bad once out of the city, there's several AI's on the East End and other places. We spent a morning and dove from one called
Sapphire Beach, it was all condos - seemed pretty nice. DiveIn has their boat at the marina there, there were 4 of us on the dive. I don't think they take more than 6 ever. As I recall the restaurant was a little disappointing - at least for lunch, however you're about a mile from Red Hook where there's a good 1/2 dozen restaurants - everything from a great dockside bar (Molly Malone's) with food to fancy dining.
hth, I've been all these places in the last couple years if you have any other questions.