Take the 101 and 1 - FOR SURE! It's the only way to do it. You'll be driving right along the Pacific much of the way, and hit everything from L.A. to Santa Barbara, Santa Cruz, San Francisco, Humboldt County and Redwood National Park, up through the Oregon Coast (hit up Florence and the sand dunes, then Newport). At Newport, I'd head inland. Corvallis is cool, Eugene in worth a stop, take the 5 up to Portland, then continue north to hit Olympia/Tacoma/Seattle. You can wind around the Olympic Peninsula on the 101 as well. As far as the eastern sides of all these states . . . ehhh. You won't be missing a ton skipping it. Notables are the Cascades, Columbia River Gorge (you can see that driving just a little ways east out of Portland - along with Multnomah Falls - a pretty cool waterfall), and maybe the caves and lava tubes in eastern Oregon (Bend is a good place to stop for that). You'll; probably want to spend a few days in each of the more major cities, can easily spend a few days relaxing in Arcata and the redwoods, drive time will be several days worth alone, and so that should cover you. Just my recommendations, but as someone from the midwest that came out here and did extensive traveling and have stuck around the past few years, I feel I've got a pretty good idea of what's worth seeing. OH, and don't forget a hot spring trip. Oregon has several worth seeing, the favorite of which I visited being Cougar (aka Terwilliger Hot Springs). Very clothing optional and friendly. Everytime I went there we had new friends to chat with while there. I've heard Umpqua has some nice springs as well. There are also tons of national forestland acres you will be near if you enjoy camping or hiking or mountain biking or whatever.
I've hitchhiked all over the west coast, hiked it, bused it, you name it, but I've seen and spent time in A LOT of places out here. I have a pretty darn good sense of what's seeing and all the things only the "locals" normally know of. You can message me if you'd like more specific ideas as far as what to do or see in any specific locale. There are plenty of touristy and non-touristy things to do in the cities, and the smaller towns have a lot of hidden gems.