The Blue Heron Center for the Arts (mid-island at Vashon Island Hwy. and 196th St. SW, 206/463-5131, www.vashonalliedarts.org [1], closed Sun.–Mon.) has a small gallery with high-quality arts and crafts, and a central space for concerts, classes, and plays.
Other fine places for artwork are Silverwood Gallery (24927 Vashon Hwy. SW, Burton, 206/463-1722) and Brian Brenno Blown Glass (17630 Vashon Hwy. SW, www.brianbrennoblownglass.com [2]).
Local art galleries are open to the public with open studios the first two weekends of May and December.
Links:
[1] http://www.vashonalliedarts.org
[2] http://www.brianbrennoblownglass.com