The town and the sites? On Vashon Island?
You'll probably want to go to Quartermaster Harbor. I have no idea what resources are there from a marina or public dock
standpoint, but there are docks there. This is on the South end of the island. It's actually between Vashon Island and the other island (to the East). I forget the name of the other Island, but if you come ashore these and meet any of the indigenous peoples, be careful when referring to is as Vashon, it has some other name that some are rather sensitive about (they are connected with a man made causeway). I'm sure if you're interested you can find a local to tell you more than you'll ever want to know easily enough.
The North end of the Island might be doable at anchor
for a short stay, but it's really exposed to North winds and gets a lot of ferry
traffic nearby. The only real beach is right at the ferry dock
and I'm not sure how keen they are with people landing there (I'm sure actually using there dock will get them very upset). But the bus stop on the ferry dock is right there and easy to get a bus to "town".