Without adding a bunch of detail (because I am sure you will get a lot of that) let me suggest, since time is no object. I would take this route: From Denver to Black Canyon of the Gunnison to Mesa Verde National Park to Hovenweep National Monument to Moab, Utah (Arches, Canyonlands and Dead Horse Point) to Dinosaur National Monument to Flaming Gorge NRA to Fort Bridger to Grand Tetons (Jackson, Wyoming) to Yellowstone National Park to Glacier National Park to Pompies Pillar to Theodore Roosevelt National Park and then straight south to the Black Hills and Rushmore National Monument. (If time is really no problem, one should not miss The International Peace Garden -- a little north of Teddy Roosevelt Park) There is no reason to stop at Flaming Gorge or Fort Bridger other than the scenery is worth the drive. Another side trip would be to take Highway 14A from the North East exit of Yellowstone to Cody Wyoming. This is (IMHO) in the top five Scenic Bypasses in the U.S.... maybe even higher on the list. (If you do, be sure to take the two mile hike -- above treeline -- to the Medicine Wheel National Monument.)
Now for a little editorializing: At the end of this Itinerary, Mount Rushmore will be a great disappointment. It is, after all, merely graffiti on the side of a mountain. It will be very crowded and very expensive. The Crazy Horse dig is less crowded, BTW, but much more expensive (high price/little to see).