I'm just on my way back from a trip up to Mount Saint Helens. After the long cold winter it's exceptionally beautiful around here. That should hold true pretty much anywhere you go in the mountains.
With a month to see the area I'd spend some time in the desert (generally eastern OR/WA), the cascade mountains, a trip through the valley (Seattle/Portland) and for sure the coast.
If you don't mind getting off-grid a bit the Gifford Pinchot forest south of St. Helens is great. Most places are within an hour or two of metro areas so they're great for day trips if you have a toad or drop a trailer or 5th wheel. And the roads aren't bad with the house attached. Just a little bumpy at times.
In general, the state campgrounds are great if you like to rough it a bit or there are lots of RV parks around.
You really can't go wrong with anywhere you go.... have fun
Don't forget Fort Rock, I believe it's in the Christmas Valley, east of 97 and SE of LaPine. There's a restaurant nearby, about 3-4 miles past electricity. 5# steaks or whole chicken grilled. One of a kind.
If you've made it this far...don't stop here, drive 45 minutes east on I-90 to Coeur D'Alene, Idaho. Check out The Coeur D'Alene Resort with the floating green.
Others have posted some great suggestions. You don't say how you are planning to get to the NW from Colorado. If you are coming in on I-84 some good spots along the way are McCall in Idaho, Hells Canyon--check out Idaho Power campgrounds, and the Columbia River gorge is beautiful--make sure to use your toad on the old road to see the waterfalls. Portland is a nice city. Light rail and the streetcar make getting around easy and it is a city of great little neighborhoods.
Most of the rest of the major sights in Oregon are arranged in two corridors--Hwy 101 along the coast and Hwy 97 on the east side of the Cascades so a loop that takes them in isn't a bad idea. The I-5 corridor is a good place to move through the state but there isn't much to see but crops until you get near California where the mountains appear.
The Oregon Coast itself is outstanding and well worth at least a week. Some people drive the length, others visit either the north or south part. Generally the coast gets wilder and the towns smaller from the north to the south as you get away from urban areas. From Portland I like to head to the Astoria/Cannon Beach/Seaside area. Lots to see and do there. Heading south we really like Cape Lookout State Park south of Tillamook. Almost all Oregon State Parks are pretty much exceptional in my opinion, especially those on the coast, you really can't go wrong. Beverly Beach, Honeyman near the dunes, Sunset Bay near Coos Bay, and Harris SP near Brookings are all outstanding state parks. Cape Perpetua is outstanding--if you can fit--only a few spots for your size.
If you haven't been to the redwoods in Northern California consider a side trip just over the border to a ton of great places. Hwy 199 is a good highway that goes through redwoods to the Oregon Caves area. A side trip to Ashland is good if you are into theater. It is also a beautiful town with good camping nearby at Emigrant Lake. Crater Lake NP is outstanding. We like to stay at Diamond Lake on the north side. The RV park is okay, but if you can live without the hook here stay right on the lake at the Diamond Lake NF campground in beautiful spacious spots. North of Crater Lake on Hwy 97 is the Bend/Sisters area. If you look on a map there is a sideways figure-eight to the west formed by Hwys 20, 242, and 126. You can only drive 242 in your toad, but it is worth it. This area has fantastic camping in the Metolius and at Belknap on the west side. Then if you drive north towards Washington try to visit Silver Falls State Park for its amazing waterfalls and trails.
Heading north into Washington Mt St. Helens and Mt Rainier are both great national parks near the I-5 corridor. Then you can head around the Olympic Peninsula on 101 in a loop. The northern part along the Strait of Juan De Fuca is packed with great towns, sights, and camping.
Seattle is a great city, but the camping nearby is underwhelming and expensive for the most part. North of Seattle within 75 miles of I-5 are Deception Pass and Whidbey Island, great inland camping in the Cascades, North Cascades NP, and even Vancouver and Vancouver Island if you are so inclined.
Spokane to the east is my hometown and is a great place. We recently stayed along the river at Riverside State Park right in town and had a blast. If you head back to or from Washington from the east through Idaho and Montana you will enjoy the park downtown there and other sights. And nearby Northern Idaho is full of great lakes to camp nearby.
You are smart to take 4-5 weeks. Two weeks in each state gives you the time to explore some great places. Good luck.
Family that loves to camp 30 days a year! Two kids, 13 and 9