There are no places in Seattle which require formal wear (or in the west coast for that matter?). The problem is - when you're on your way to your table, the other diners might ask you for a cup of coffee or something. :-)
Closest place you can still "dress up" and not feel too out of place may be the downtown steakhouses (Morton's, The Met, Ruth's Chris, El Gaucho, etc.) Canlis too, I suppose.