You might want to give them a call:
Bellevue Arts & Craft Fair
Bellevue Arts Museum
510 Bellevue Way NE
(425) 519-0770
I would guess if it's indoors and there's pricy art around, that they might not be so welcoming of doggies?
Sunnie: Oh, Seattle is a GREAT dog-friendly city! You can take your furbabies to Nordstrom's at least.
And there's a lot of parks and places for Yorkies to walk as well! The weather is very nice and pleasant this time of year! Enjoy it!