No beaches within walking distance of the cruise ship dock in St. Kitts. The nearest beach with "facilities" (beach bars, restaurants, chair/umbrella rentals and water sports) is Frigate Bay (10 minutes by taxi). Other beaches with facilities are South Friars (15 minutes by taxi) and Cockleshell (25 to 30 minutes by taxi). No other beaches around the island have "facilities". All 3 mentioned will have their fair share of your fellow cruise ship passengers.

Off beach snorkeling on St. Kitts leaves a lot to be desired. Best snorkeling is a Shitten Bay which is accessible only by boat. Excursions leave from the Marina adjacent to the cruise ship dock. You can book excursions and/or day sails at the various kiosks in the shopping complex just outside the cruise ship dock.

Can't give you specifics about Antigua other than to tell you you'll find plenty of tour operators/vendors hawking their excursions near the cruise ship dock. Lots of beaches around the island to choose, many have beach bars, but like St. Kitts, off beach snorkeling is not plentiful. You need to book a boat excursion to reach the better sites.