So I think you should choose either a "Southern" trip, or a "Northern trip", not both. The rest of this post is a possible "Southern Trip":
Colorado: I wouldn'twaste time at Pikes Peak, get out West towards the Crest and the San Juans instead-- Silverton to Durango, maybe via Gunnison "Black Canyon" and Montrose and Ouray). Continue Southwest, see Mesa Verde on that route and work your way through AZ or UT to Grand Canyon, Las Vegas. DON'T miss touring Hoover Dam. (Zion/Cedar Breaks and Bryce should probably be included on the way to or from Grand Canyon-- could be on the way back, unless you want to see "Northern Utah sites too.)
Unfortunately, I don't think you have enough time to go WAY out of the way South for either of the two great Southwest caves (Karchner caverns, Southwest of Tuscon, or Carlsbad, New Mexico). You probably haven't heard of Karchner, because it wasn't discovered and developed until about a dozen years ago, and it's "merely" a State Park-- but it's JUST as incredible.
After Vegas, you might want to go to LA. Good museums, famous landmarks-- the Griffith Park Observatory has just been restored. I'd take go up the coast (101 towards Highway 1), and do the usual CA coastal things: Santa Barbara, Hearst Castle, Big Sur, Monterrey, up to Frisco. Although Unfortunately, summertime State Beach camping spots are tough to get on short notice. US-1 will be very slow in tourist season, I think it's worth it-- but you might not. The big problem with skipping it, though, is missing Hearst Castle-- Hwy 1 is the only way to get there.
If you want all Mountains and no Oceans, don't go to LA. But I think either of the South to North mountain routes are just more of the same, you've already seen big hills and pretty granite in Colorado. (Tthe west side Sequioa/King's Canyon/Yosemite thing, which need reservations done a long time ago, or the East side up 395-- much less crowded, great scenery at places like Whitney Portal, Devil's Staircase, etc, but lots of dull "empty" spaces too.)
And Highway 1 gets to San Francisco without crossing the central valley again. There's nice places to stay in towns like Santa Cruz. After Frisco (over the Golden Gate, of course) there's more coastal action, and maybe a detour inland to wine country, if you're so inclined. (I love the wine, dislike the "wine country".) Going North on the coast, maybe even all the way to Crescent City, there's plenty of great beaches. And since you missed the Sequioas, don't miss the tall redwoods, in Redwoods National Park.
Next comes a hard choice: to go to Crater Lake on THIS trip, or do it as part of a "Northern trip" another time? If you do proceed into Oregon, ALL of the drives across the Klamath mountains are nice, take your pick.
And both the North Umpqua (138) and Rogue river (62) routes to the park are superb.
That's a very suitable turnaround point. I'd start back towards Klamath Falls (Lava Beds National Monument), then 139-229-89 into Mt. Lassen. Leaving the park, continue on 89 through Quincy and down to I-80. (There's great RV parks along there, near Graegle and Blairsden). At I-80 you
probably want to go and see lake Tahoe-- although, so soon after Crater lake, you'll probably be disappointed! (Crater lake is WAY more blue and WAY more pristine.)
Now, you're basically stuck on the wrong side of Nevada. (As I've been stuck here for years
) The route out depends on whether you want Salt Lake City and higher Mountains in Northern Utah, or the strip of "Grand Staircase" and Canyon parks along Southern Utah. Within Nevada it's no contest, US-50 is much more scenic. Do NOT miss the "Grimes Point" petroglyph area just past Fallon. Ely is a nice destinaton, and if you prefer hookups, its' close enough to use as a base for Great Basin National Park. Cross into Utah and visit the String of National Parks (if not already seen on the way out), ending with Canyonlands and Arches. Back into Colorado via Grand Junction. This time, I'd stay on the freeway for a while. If you want some extra high Country, a cetour down to Leadville is fun. But after the Eisenhower tunnel, you'll be going North on 40, into RNP at Granby. (Trail Ridge Road is nice, VERY nice. I think Long's Peak is a lot prettier than Pikes Peak, too). I'd go down to Denver via highway 7 approaching Long's peak close, going through Boulder (Ritzy college town), and then going into town via Central City and Golden.
Denver's nice. After that, you're on your own-- I've never been in the flatlands east of there.
Now as you see, I didn't even get to Yosemite. Or Mt. Shasta. Or San Diego. And it looks like a really "heavy" month of traveling to me, running around really fast. But if you request, I'll follow up with a similar post about how I'd route a month-long tour of the "Northern" US West. I'll start in South Dakota, because I've never been in Nebraska on vacation.