AZBuck has a good route, but I want to suggest a few alternates that are right along his route.

Instead of Rocky Mountain NP, Try Mount Evans, a paved and very scenic route out of Idaho Springs, CO. It is higher than Pikes Peak by a few hundred feet, too, and is only twenty miles off I-70. Up 103.

In Utah, get off I-70 at Cisco and drive Ut128 down through Red Canyon to Moab. You'll follow the Colorado River with spectacular scenery, and the entrance to Arches NP is only a mile or so up 191 when you get to Moab.