I am not familiar with the neighborhood but there are probably some very good airbnb values in this changing area. Some new restaurants are opening here to great acclaim, I haven’t had the chance to investigate much but if you pull up a google map of the area you will be able to see the restaurants in the area. One that is particularly good:
Bar Del Corso–you will need to call ahead and ask GF questions (we did not have our celiac children with us when we ate there) but there are many small plates and salads, charcuterie, and soft cheeses that seem naturally GF–along with a nice wine selection and craft cocktails–all that should be plenty without even thinking about the pizza on a wheat crust. The pizza prep area is completely separate from where the small plates and salads are prepared.
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.