Having to spend several days in Seattle for work, I discovered a wonderful AirBnB rental (highly recommended!) that is economical and perfectly situated for gorgeous, scenic runs. If you're headed to Seattle, I encourage you to stay there (and tell Laura I sent you). While you're in the neighborhood, definitely check out nearby Carkeek Park, whose mixture of forested, hilly trails and breathtaking seaside offers the best of the Pacific Northwest.
From the AirBnB, you first take a loooooong run downhill on NW 116th Street, where you get this awesome view:
As you run down 116th, keep an eye out on the right for a forested path that leads to Carkeek Park (this spares pedestrians from having to share a narrow road with cars). From there, miles and miles of trails follow!
I'd planned to explore more of the trails around Seattle, and on future trips, perhaps I will. But for this busy traveler with little time to drive to some other trailhead, running down the hill each morning I was in town was a fun adventure, and a wonderful way to start the day.