Almost all of Vashon Island's businesses and restaurants are located in the town of Vashon. One exception is the Back Bay Inn, in Burton on the southern end of the island. It has changed ownership since my last visit, but it is known as a place to go for quality, fairly upscale dining.
It is also a B & B.
Ok, well I don't know if I'd actually call it a restaurant. It's at Nana's house. There's only one table (her dining table just off the kitchen). You will be the only people eating there and Nana will watch tv in the other room until you ring the little bell she gave you. I've only been there once with a good friend and we had a blast. Not necessarily because the dining was so great, but because it was so random that we found it amusing. Nana made us pork loin which was pretty good. I don't think you get much of a choice though. She makes what's in the fridge. So, it really IS like eating at your grandma's house. It's BYOB, but Nana doesn't charge a corkage fee. :-)
*By reservation only!