Given your short time in Bermuda (about 8 hours), if you'd like to visit Hamilton or St. George, I'd either recommend a ship's tour or take the ferry over first thing. A ferry schedule is located here
, but be sure to pick up a current one when you are there. There's not a whole lot to occupy your time at King's Wharf, unless you want to go helmet diving or visit the maritime museum. It is a pretty neat area to walk around, though, but IMO it's not the "real" Bermuda.