The harbor is long and shaped like a reverse question-mark. There are a couple places to stop along the way (Burton Acres Park and Drayton, both with restrooms), and once we got all the way up to the end of the harbor, we got out on a float and walked into town to the store. There really isn't a great place to stop in ton, but my experience is that you can usually find a float at the marina for a short period.
It is possible to paddle right to the isthmus that connects Vashon and Maury Islands, get out of your kayak, and portage to the out side of the island. It's about a 100-yard walk and it is a great way to circumnavigate Maury Island. Allow a whole day from Tacoma though.
We didn't have that long, so we followed the falling tide back out of the harbor and paddled back to the beach at Point Defiance. Great trip!