A lot depends on your specific driving route, but I'm going to assume SF as a starting point and Durango CO as a mid point, after which I don't have any suggestions for you.
One option is SF -> Yosemite valley -> over Tioga pass (with a stop in Tuolumne Meadows) -> Mono Lake -> long drive through NV -> Zion National Park -> Bryce Canyon National Park -> North Rim of Grand Canyon National Park -> Vermilion Cliffs -> Monument Valley (mixed reviews, but may be worth a short stop) -> Durango Sorry, I just noticed that you're going in April...Tioga pass typically doesn't open until end of May. You can still kinda do this route, but not Tuolomne Meadows or Tioga pass, and you'll have to backtrack either north to Tahoe or south to Tehachapi (or hwy 178) to get around the Sierra Nevada high country. Oh, and the North Rim of the Grand Canyon may not be open in April. You could make the drive around to the south, though that's a pretty long detour :(
Or, another option is to go a slightly more northern route: SF -> Tahoe -> Virginia City, NV (maybe?) -> long drive through NV via hwy 50, the "loneliest highway in the US" -> Great Basin National Park (be sure to book a cave tour, and make a point to do some star gazing esp. if you're staying at the high elevation campground) -> Arches National Park -> Canyonlands National Park -> Canyons of the Ancients National Monument -> Durango