Ceud měle fŕilte! Welcome aboard the RoadTrip America Forums!
First of all, relax. It is quite possible to include everything you've mentioned, and more, into a month-long RoadTrip of the American southwest. Let's start with just a rough outline of those places and some scenic routes to connect them. From San Francisco, your initial destination should be Yosemite. Early spring can be an ideal time, if still a bit chilly, to see this park. The tourists will not have started to clog the roads and viewpoints, but if the spring melt has well and truly started the falls will be spectacular. From there bead back to the coast around Monterey/Carmel and head south along the Pacific Coast Highway (PCH, CA-1) through Big Sur, San Simeon (Hearst Castle), and Cambria. You don't mention Los Angeles in your wish list but it's possible. More photogenic are towns just northwest of there such as Solvang and Santa Barbara. In any event, from around that area, head inland to I-15 and head up to Las Vegas. While there, you might want to do a day trip up to Death Valley which will be 'relatively' cool at that time of year.
After your stay in Las Vegas take US-93 south over the Hoover Dam to I-40 east. You can take the opportunity to drive one of the longest remaining stretches of old Route 66 (now marked AZ-66) from Kingman through Peach Springs to Seligman. Note that this stretch of road furnished the visual inspiration for the animated movie "Cars". At Williams, leave the motorway and take AZ-64 up through Grand Canyon National Park. Leave the ark to the east and take US-89/US-160 up to Monument Valley. Try to see Monument Valley at sunrise or sunset, and splurge on the 4WD, native-guided ride. Next, use US-163/US-191/UT-162/CO-41 to return to US-160 and Mesa Verde National Park. To see some of the best of the Rockies head north on US-550 through Durango and Silverton to Montrose and then US-50 through the Black Canyon of the Gunnison to Poncha Springs, and finally US-285 into the Denver area. While in and around Denver, get up to Rocky Mountain National Park.
For the return from Denver back to San Francisco, you can fly of course, but that adds a one-way drop-off fee to the cost of the car rental, and the cost of the internal flight. You can just as easily, drive back to San Francisco on I-25/I-80 in three relatively easy days via the Great Divide Basin, the Great Salt Lake, the Basin and Range province of northern Nevada, Lake Tahoe, and the Sierra Nevada. I f you do end up deciding to fly, note that there are a few lower-cost airlines that service that route that will not show up on search engines: Southwest and Frontier are the main ones, although you may have to fly into a nearby airport such as Oakland or San Jose.
That should give you a bit t chew on for a while. There are many more attractions that you could easily fit into such a routing, but let's get the basic framework set up first.
AZBuck