you can tour puget sound to portland any time of year; the trip is lowland, and it never really freezes up here except the dead of winter (right now, hard freezes for the last week and temps subfreezing).
I've ridden to portland as early as easter; right now you'd be looking for places to camp no later than 4 pm as its' getting dark about 4:30 or so.
the best time would be sept-oct but id suggest you don't wait that long, its very nice riding, quite pastoral and idyllic betwixt the two cities. you could do it in 2 days, camping around mima mounds,
or 3 days and take it easy, utilizing hotels in olympia and longview.
if its summer, and you are ambitious, you can ride an excellent volcanoes tour around mount adams, helens and rainier on a trip between seattle and portland, but thats 4 days, lots of remote, gravel, and pass climbing- not a viable off season trip.