In a couple of weeks I will be taking a cruise and one of the stops will be in Tortola. Is there a beach walking distance from the pier?
There is not Brewers Bay and Cane Garden Bay are nice beaches near by (crowded, though) but both will require a cab ride
Tortola is not really a fun port stop. About all that is accessible within walking distance of the pier is Road Town which is pretty gritty. Rum is cheap at the supermarket up the street from the old prison.
Are you familiar with cruisecritic.com? You can go on there, click research, then "destinations". It will have all that sort of information.