As a lifelong corporate aviator I have flown into Vegas several dozen times for company trade shows.
Vegas is a great staging point but many hundreds of miles and weeks of time required.
Here is a short list of many of the places that are a must see and how I got to them.
You might want to plan one big circle to hit as many of them as you can.
West out of Vegas to Death Valley then over the mountains to 395.
North on 395 to Bishop ,Lee Vining and then Monolake.
West over the Sierras to Yosemite.
Southeast from Vegas down to route 66. East to Williams then north to the Grand Canyon.
Northeast to Page and Antelop Canyon. East a few more miles to Monument Valley.
Northeast out of Vegas on Route 15 to Zion and Bryce Canyons. If time permits further northeast to Moab.
A month is needed to hit all these spots.
Have a great trip.
Ps. After reading my post all the north,south,east and west directions look a little out of place.
Only another pilot would understand.
When my wife and I are on one of these road trips she often asks me why I spend so much time looking at the skyline and the ridges. I just tell her position awareness. She knows what that means.