Wow! What a great trip you have planned!
You got room for another passenger/driver? LOL
Brad's right. I've tried to get "Welcome to...." shots of my car at each state crossing and some are in really bad places making it precarious and even dangerous to do so. Of course, there's lots of points of entry into each state so you might have better luck than I have so far.
Some ideas:
Washington: Mt. St. Helens, Wild Waves/Enchanted Village (since you're theme park junkies), Pike Place Market, Space Needle, Seattle Waterfront with a ferry in the background, Mt. Rainier, Olympic National Park
Oregon: Crater Lake, The Oregon Vortex (not quite a theme park but very strange and fun like one), anywhere along the coast but Depoe Bay is a favorite, the Sea Lion Caves, the Oregon Dunes National Rec Area, Mt. Hood, Columbia River Gorge Vista House
Idaho: Silverwood Theme Park (some of the biggest wooden roller coasters in the world), Craters of the Moon, Hagerman Fossil Beds, Shoshone Indian Ice Caves, Snake River Canyon...look for the infamous ramp where Evil Knieval attempted his crossing by motorcycle/rocket near Twin Falls
Montana: Glacier NP especially the Going to the Sun Road, Big Timber Waterslides, Greycliff Prairie Dog Town, Copper King Mansion in Butte, the museum in Bozeman, MT, at the university there with all the great dinosaur stuff found by Jack Horner (Jack Horner is who the paleontologist in "Jurassic Park" was based on), Little Bighorn Battlefield
Wyoming: Yellowstone NP, Grand Teton NP, Cody is a great "wild west" town (check out the Buffalo Bill Historical Center there), Fort Laramie, Devil's Tower
Utah: Wow, so much. You can't go wrong with any of these national parks - Zion, Arches, Bryce, Canyonlands, and even a few more I haven't mentioned. Hole in the Rock (south of Moab), Dinosaur Nat Monument (also in Colorado), Golden Spike National Historic Site, there's a theme park in Salt Lake City but I don't recall the name of it (I didn't have time to stop there but it looked pretty good from the highway).
Colorado: Glenwood Hot Springs (largest outdoor mineral pool in the world), Leadville (just a really cool mountain town and the only incorporated town at this elevation, the air is thin up here; eat at the wonderful Quincy's), Durango (wonderful mountain town, take the train ride if you have time), Mesa Verde, Rocky Mountain NP
New Mexico: Albuquerque (the historic district is wonderful and the view driving toward the city with the huge mesa behind it is stunning), Roswell for all that fun alien stuff, Carlsbad Caverns, White Sands, Fort Lincoln area and the Billy the Kid stuff there, Smoky the Bear's grave, the Very Large Array (as seen in the movie "Contact"), Gallup & Tucamcari (both great Route 66 towns)
I'll leave the rest of the Southwest for our many contributors who live there. Hope this gives you a good start on ideas.
If I were you, I'd google "(state name) tourism" for every state and start browsing for ideas. For each state, request their free tourism information. You'll get a wealth of free information from both of these sources.