It's a small city, about 24,000 people, and much of the island itself is pretty rural. But in the main area of Winslow, by the ferry dock, there is a thriving community of families, artisans, and local business owners.
I've always loved living on Bainbridge Island, partly for the views; you can see everything. The Olympic Mountains to the west, Puget Sound in all directions, and the city scape of Seattle to the east - all of these things have their own beauty. There are a number of museums, galleries, and parks; the school district is good and apparently the kids' sports teams are terrific. There's a biking event called the Chilly Hilly every February, and it kicks off the Pacific Northwest's cycling season.
Being in the middle of Puget Sound, the seafood here is wonderful. There's quite a lot to do on the island itself, with or without children, but if you're looking for fancier opera or professional sports, Seattle is just a ferry ride away.