I have sailed into King's Wharf before on Celebrity and it is boring. There are a couple of stores, etc. It is an old dock yard so there is an old building/museum there which is nice but after you spend 20 minutes looking at it your ship is still down at that end of the island. (It is a haul to get to Hamilton from there as it is on the other end of Bermuda.) They do have a cool pub/restaurant right there in the dock yard called the Frog and Onion. I had a great time hanging out in there every afternoon as it was about 80% people from our ship.
The good news is that our ship did offer 'ferry' service to and from Hamilton and St. George several times a day so if we wanted to go to one of the cities we didn't have to figure out the bus system. (Though I did that once and it wasn't too tough at all.) My advice: don't take a cruise that goes only to the Royal Navy Dockyard. It won't be bad if you only spend a day or two there and then your ship moves on to Hamilton - as I know some do. But the entire time there is boring.