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Cruise ships really drop off in April, May and June. We are travelling in Late June early July for 10 days and there is only a cruise ship twice during our time. Cruise ship activities also tend to focus on select places with the busiest of them on Tortola (Cane garden bay is a mess, Sopers Hole is pretty busy) with more traffic on some of the other islands (the Bight Norman Island had some cruise people and White bay.)

You can still escape the crowds if you are in Virgin Gorda, North Sound, Anegada would be fine.

Also keep in mind that cruise ship activity is really limited to a limited to between 10-4 or so. And then they clear back to their boat and off to their next location. You can still have a great time at the beach before or after and enjoy the sunset and a much nicer atmosphere and night life at Cane Garden bay or Great Harbour on Jost.