Snohomish County is north of King County and does not have any suburbs of Seattle. Seattle is in King County which ends at 205th Street north.There is no pasture starting at 205th Street, just a continuous block of "cities" including Brier, Lynwood, and Edmonds.
You do know suburbs aren't contained by counties, and can even extend across state lines, right?
For example (from Wikipedia, but valid nonetheless): "Vancouver is a city on the north bank of the Columbia River in the U.S. state of Washington. It is the largest suburb of Portland, Oregon".
I always think of Edmonds, Lynnwood and Brier as suburbs of Everett, the largest town in Snohomish County. But I guess they could be considered suburbs of Seattle.
I live just shy of the Snohomish County line in King County. The taxes are less in Snohomish County so I wish I lived there instead of in King County.