In Tortola only 4 hours total; in the morning, obviously not worth to venture out far from ship. Anything close to port walking distance; or any beach max. 10 minutes taxi drive?

There is a nice beach that is about 10 minutes from the port by cab. Ask one of the locals to take you to the beach by the restaurant where Jimmy Buffet wrote Cheeseburger in Paradise (according to the driver we had). There are plenty of taxis waiting for you outside the port. They do have some shopping near by as well. Too bad it's not for longer, there's some great snorkeling over by Norman's Island. It's a 4 hour excursion on a dive boat, but it's really good snorkeling for the next time you're there. Tortolla is a great island. Have a wonderful cruise!