Ok, you've got three days to cover a thousand miles. It'll take two days on the interstate as long as nothing major goes wrong: the days are long and you'll be full of enthusiasm about your big trip.
That leaves a day to spare, or maybe two days if you actually leave on the 22nd (but preparation and packing tends to take longer than you think--ask me how I know this). You can spend your extra day taking less-efficient roads--the ones with all the fun curves and scenic views on them--or you can spend it visiting Tukwila and maybe a few other places along the main route. Either way, you've got to hustle to Vancouver.
Personally, I'd make it a motorcycle trip rather than a museum trip. That means three full days in the saddle. I'd follow the coast highways if the weather forecast looked good: Highway one and 101 the entire way until I ran out of time, then cut across wherever is convenient to Interstate 5 and follow it through the border to the airport or the port. I'd make a point of stopping in one of the redwood parks for a stroll, eat lunch on one or another beach in Oregon viewing sea lions, and hope I had time to check out the Hoh rainforest, Hurricane Ridge, or the beaches in Olympic National Park. In the end you might find you've got to skip the Olympic Peninsula entirely due to time constraints. Don't forget to allow for the ferry ride from Port Townsend or Port Angeles (and if the latter, another ferry from Victoria Island).
If the weather looked gloomy, I'd definitely plot a route up the east side of the Cascades: the string of volcanoes includes Lassen, Shasta, McLaughlin, Crater Lake, The Sisters, Jefferson, Hood, Adams, Mt. St. Helens, Rainier, Baker. But first you'll need to find out which roads are plowed out: Rt. 20 (the North Cascades Highway in WA) just opened, the Lassen Park road will probably still be snowed in, and everything in between is up for grabs. That route doesn't include the windy roads you'll find near the coast, but there are ample little side trips if you like mountains and can figure out which ones are plowed and open--Lassen, Crater Lake, the Cascade Lakes Highway, Rt. 242 in OR, Timberline, the roads around Rainier, the North Cascades Highway are all great.
There are campsites everywhere if you're just a bike and a tent, and paid campgrounds everywhere else. Don't even worry about this, although do be prepared for the crowds and elevated prices in (especially) California State parks.
Don't forget to leave some extra time to package up thirty pounds of stuff you realize you don't really need and send it home.
I'll say again: you're going to be rushed, and you'll have time to do hardly anything at all aside from ride ride ride. Come back again someday with some more time.