I generally use JFK or LGA, but HPN is a nice airport also.
The first time I stayed at Sunset Shores, and the second time I stayed at Mariners. Both hotels are good for divers. It's just a matter of which one is available. I would have to check my invoices but they were both relatively the same price.
For both dive trips, I booked the hotel and dive package through Dive St. Vincent. They organized airport transfer, hotel w/breakfast, and of course, diving.
In Bequia, I dived with Dive Bequia. Getting from St. Vincent to Bequia is super easy and the ferry system runs on time. I stayed at the Lookout Villa, which is a 5-10 minute drive taxi ride from the dive shop, and it took me about 1/2 hour to walk back without gear. I ended up making a deal with the taxi driver to pick me up each morning. There are hotels that are much closer to the two or three dive shops on the island. However, when I booked, there was not much availability. It's a small island so things seem to book pretty quickly during peak periods.