Bainbridge is nice, but i havent stayed anywhere on the island. I actually have lived here 43 yrs and never been to Vashon.
A really nice place to stay, but it may be too expensive is North Shore Cottages on Orcas Island.
Welcome to North Shore Cottages on Orcas Island
Its not a island, but Poulsbo has some really nice things to do, or Port Townsend across from Whidbey Island has a lot of neat things to do and great history.
Manressa Castle is great, or the Palace Hotel. They filmed A Officer and a Gentleman close by at Fort Warden, and The Tides Inn, they remodeled the hotel since the movie though. It doesnt look anything like it did.