This trip requires a minimum of 11 nights/12 days, but two weeks or more will make for a much better trip. Here’s a framework for an itinerary to go with the map:
Leave LV and head to Zion for 2-3 nights.
On to Bryce Canyon for 1-2 nights
Take the day and enjoy scenic route 12; overnight in Torrey.
Explore Capitol Reef and Goblin Valley on the way to Moab. Or take all day in Capitol Reef and spend a second night in Torrey. Next visit Goblin Valley and perhaps hike Little Wild Horse and/or Bell slot canyons on the way to Moab.
2-4 nights in Moab (Arches, Canyonlands Island in the Sky, Dead Horse Point SP, drive route 128 and the La Sal Mountain roads, mountain biking, rafting, day trip to the Needles section of Canyonlands and Newspaper Rock….lots of options).
South to Monument Valley for a night.
On to Page for 2 to 4 nights. Again many options on how to fill the time (Antelope Canyon, Horseshoe Bend, raft trip, boating on Lake Powell, lake tour to Rainbow Bridge, tour the dam, Lee’s Ferry and Navajo Bridge…you get the picture).
On to the Grand Canyon south rim for at least one night…more if you plan hiking below the rim.