If your month includes the drive out and back (2500 miles each way) you're really down to less than three weeks. Last trip we took to the coast we just did the southern half of the Oregon Coast and from here (1200 miles one way) in a month, just to give you an idea of timing. You'll be happier if you can squeeze another week or two into this trip.
So many places have been mentioned. With such limited time, I'd suggest either Mt. Rainier or Mt. St. Helens. The Columbia River Gorge has lots of waterfalls on short to intermediate hikes, but some areas were heavily burned a few years ago. Ainsworth SP in on the south side of the river and has FHU. Of course there's Crater Lake. With your limited time, I wouldn't try to get to Oregon Caves.
For ocean kayaking, I might suggest the area around the San Juan Islands. If you're looking for river kayaking, head over toward Bend and hit the Deschutes. While there, you can also visit Newberry Crater. Camping there is like camping along the shores of Crater Lake - you're at the bottom of a volcanic crater.
If you can, drive the Oregon coast from north to south so you can more easily slip into scenic pull offs. The northern part of the OR coast is the more touristy and busier part of the coast, the southern part is less crowded and maybe more scenic IMHO. If you're interested, there are some lighthouses along the coast you can tour.
brochure If you camp at Harris Beach SP way south along the coast, you can day trip into northern CA and explore the redwoods there.
OR state parks are kind of the gold standard for SP's in this country. Sunset Bay SP outside of Coos Bay has an interesting setting. Beachside SP is just what is says. A couple of miles down the road, Tillicum Beach SP is also right on the beach.
WA also has some nice parks. We stayed at Deception Pass SP when we day tripped out to the San Juan's by ferry.
Once you start to get a plan in place, post more specific questions. And consider getting reservations at the SP's along the coast when they open up as they fill quickly. I think it's a rolling 9 month window.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)