Dros, sounds like a fun trip. Here are the 3 basic choices (with lots of possible variations) on route, with the relative merits/demerits of each:
1) up the I-5 corridor into Seattle, ferry to Victoria (STP route):
shortest distance, Victoria Clipper ferry is kind of spendy ($50+ i think one way), and who wants to ride through suburban Seattle?
2) up the I-5 corridor, at Olympia go up the west side of Hood Canal/east side of the Olympic peninsula to Port Angeles ferry:
a little longer than Seattle, more scenic, ferry reasonable ($10 or so), but this part of hwy 101 along Hood Canal has never looked appealing to me (I've driven it many times) from a traffic/shoulder width perspective: too much of former, not enough of latter.
3) to the coast, and up the coast & around the west/north side of the Olympic peninsula to Port Angeles:
considerably longer but very scenic. Not much traffic. Some great camp grounds en route. rode this a few years back & really liked it. Can shorten the trip by Amtrak'ing to Centralia, and heading out to the coast from there. Still, it's a good 4 days if not 5, depending.
The Washington state bike map is a good resource for planning this, even though I've found the info. on shoulder width to be undependable in places.
for order info: