If you are visiting the University of Washington you might want to stay in an Airbnb near campus to get a feel for the community. Montlake is a bit south of the U district but you could easily walk from a house there to Husky Stadium for a football game and save yourself the headache of trying to park for the game. People generally walk quite a ways to get to the stadium.
Saturdays 9am-2pm, year round. Check their website for vendors. This is the granddaddy of them all with the greatest variety of vendors and the longest history.
Aguaverde Café and Paddle Club –plan to eat lunch here either before or after you rent kayaks to explore Lake Union. Their deck is situated on the water and their food is fresh (their menu has GF notations). Their kayaks are either singles or doubles and super lightweight and easy!! Don’t miss this.
Seattle has a lot of “gluten free” people– so restaurants understand the diet to some degree– but to clarify your risk of possible cross contamination you should ask questions because every place seems to have their own definition. We have successfully dined at most of these places without issue, those we haven’t tried are so noted.