Hwy 50 from Colorado Springs (Cos) to Sacramento is one of the most beautiful roads in America. Well maintained and helpfully annotated, I'd suggest taking several days (or several return trips) to do it justice. If you appreciate mountains, rivers, clouds and sky, you'll love this trek. You can enjoy the scenery as you drive, but there are many, many opportunities to get off the road and much closer to the terrain.
Best time to go? I'd say, late spring and early fall. Sometimes Hwy 50 can be closed in the winter in Colorado and Utah. In early June, you'll have a chance to see wild flowers.
Moab, UT, is the place to stay for Arches Park. For Great Basin, Baker NV is quaint but small; if too small, try Ely, which is only about 45 minutes to the west.
Watch your gas; have snacks & water in the car -- they don't call this the loneliest road in America for nothing.