King's Wharf is located at the far west end of the island, also referred to as Dockyard. There are a few things to do at Dockyard, and you can get to the rest of the island easily from there.
Dockyard has a small enclosed mall with a few shops. Check out the Picturesque gallery for some beautiful photos of the island - the prints themselves are not cheap - but you can get a set of coasters or book of 20 postcards (which frame beautifully) relatively cheap.
There are several shops that are not located in the mall: a pottery, a glass-blowing factory, a few restaurants, and a craft market.
The Maritime Museum offers a neat look at the history of the island.
Dolphin Quest is an interactive, swim-with-the-dolphins experience.
There is a snorkel park where you can, well, snorkel.
There are no organized tours to speak of in Dockyard.
As I said, you can get to the whole island from Dockyard - if you want to go to Hamilton, the capital of Bermuda, take the ferry - you should be able to get passes on your cruise ship. I recommend that you buy the pass instead of doing the pay-as-you-go, since the passes are good for both the ferry system and the bus system. And you will need the bus, because this should be how you get to the beaches (you can also rent a moped, but I do not recommend that). Take the #7 bus marked "Hamilton" - the bus stop will be about a 1-minute walk from your ship - sit on the right side of the bus for the best views of the beaches - there are a ton of them - tell the driver which beach you want to get off at, and they will let you know when you are there. The most famous beach, and the one that most everyone on the bus will head directly for, is Horseshoe. I tend to stay away from Horseshoe for that reason alone - too crowded. Go up the road a little to Warwick Long Bay - it is my favorite beach.