I think andros would be your best bet but I would also look into eluethra and bimini as well

I've only been to New Providence (Nassau) a few times as well as Long Island, so I can't speak to the other out islands, but here's my Long Island trip report w/tons of info and photos if you want to look into things to do on Long Island more. We enjoyed it! If you go I'd recommend staying at Cape Santa Maria. It's beautiful.

http://www.fodors.com/community/caribbean-islands/long-island-trip-report-223-32.cfm

Do you have a budget?
What classifies as "best accomodations" to you?

The Out Islands are many, with different personalities.

Overall snorkeling is just okay, with Andros topping the list. I found Eleuthera had some spots too.

I personally think San Salvador has excellent snorkeling, and one of the prettiest beaches you'll ever lay eyes on. There's only Club Med to stay at, and includes the flight from Fla on Spirit Air. The food is also excellent. This may be what your looking for.

Abacos are terrific sailing grounds. Exumas are terrific hopping the cays with stunning beaches. Harbour Island is quant and chic at the same time. Eleuthera has stunning "rustic" beaches, but there are long stretches so hard to do in 4 days.

Keep in mind, other than San Salvador, most Out Islands may require an overnight in Nassau-they're actually pretty hard to get to.

We stay in Hopetown, Elbow Cay. It is the cheapest and safest place on earth to rent small speedboats. The snorkeling is good in many places (we frequently encountered dolphins in the wild).

Hopetown Harbour Lodge offers good food and rooms.

There are many small airlines which service Marsh Harbour and we always manage to make it to Hopetown in one day from Manchester, England.

Each island is very different and other than Nassau, it would be hard to go wrong with what you are looking for.

Long Island and Andros are not great

Have flown my own plane all over all the Islands

down there for over 30 years.

runawayhill.com Harbor Island Abaco Treasure Key my favs

atlantis.com Ocean Club Paradise Island for more touristy

upscale action.

Best diving UFO watching from the AUTEC base down there

does go to Andros Small Hope Bay Lodge AWESOME diving

Hand feed 500# groupers and do reef bounces from a

reef shelf down into the 6000 ft "Toungue of the Ocean"

Andros is best for serious divers not much else going on.

Happy Planning,

www.smallhope.com/DiveSites.html

Best for diving for me

Harbor Island best for PERFECT pink sand beach romance for me

Snorkel dive pretty nice around there shallow

usually go with Velentines there good operation.

www.valentinesdive.com/snorkel.html

Travelled to Abacos, Eleuthera, Exuma, Harbour Island, Treasure Cay and Long island. They all are somewhat unique. Abacos (elbow cay/Great guana cay etc) are nice but the main attraction is renting a little boat and exploring the surrounding cays. Eleuthera is known for its wild and plentiful beaches. HI off of Eleuthera is more chic/hip - only 3 miles long with one wonderful pink sand beach (not for us). Exuma slightly less rustic than eleu, with several nice beaches on the main land with options to rent a boat and explore surrounding islands (absolutely not necessary because there are several gorgeous beaches on the mainland). Lastly long island, is long, and off the beaten path (more like eleuthera). Cape santa maria beach on LI is simply spectacular. Other beaches to explore on the wild atlantic side as well as the caribbean side. Also known for its spectacular blue hole. I don't think you can go wrong...its a matter of picking the best one based on what you are looking for in your vacation.