Depends on where exactly you're gonna be. If you're gonna be north of downtown, you might look at Paine field (KPAE), there's are a couple of FBOs that'll be happy to check you out in one of their aircraft. I'd suggest you bring your passport and plenty of money. If you're in downtown proper, look at Boeing Field (KBFI) or Renton (KRNT) same story for both of those locations. Further south, you have Pierce County (KPLU), or Tacoma Narrows (KTIW), same deal. As far as I know, they're all similar in price and availability, though if you ask them, they'll each tell you why they're the best.
By the way, if you're actually gonna be well north of Seattle, at KBVS, about 70 miles north of Seattle's Ship-Canal-Bridge, there's an outstanding little FBO called Cascade aviation. My friend Ken Davies runs a nice little organization, with friendly staff and instructors. His fleet isn't shiny and new. But, they fly well and are well maintained.