We flew into Vegas on a 3.5 week family road trip a few years ago.
North east into Utah and Zion, then on to a load of amazing places - most mentioned here.
You've chosen an absolutely ace place to go - just unreal.
One thing I will say is that the driving there is so easy compared to here; flat, straight, empty roads - easy to drive 2/300+ miles compared to the same distance in the UK.
Monument Valley for me was the mega-highlight. Just unreal to be there. I'm getting a bit emoshe just thinking about it now. We drove in from the South (it was difficult getting accomplished anywhere near but we stayed in a fabulous wood homestead type place maybe about 30/40 miles away but no problem driving) and left up North towards Mexican Hat.
Sun going down, we drove along the road you see in the pictures and stopped to look back...just astonishing.
Drove up this tiny little mountain road about an hour away and climbed up some more to view it from maybe 20 miles away...just thinking about that now is pretty moving tbh. A family adventure, the 5 of us just experiencing the amazing.
Ended up in New Mexico which was my fave state on that trip, but not sure if you're going that far.
Through Albuquerque just because it was in that Prefab Sprout son, route 66, wanted to get to Tucson, Arizona just bc it was mentioned in that Beatles song, but was just that little bit too far so stayed in Phoenix instead.
Grand Canyon south and even a night across the river in California just for the sake of it on the way back to Nevada.
Amazing days. Buy the appropriate Rough Guide/Lonely Planet and enjoy the prep. Get things planned and then go rogue when you fancy.
Old fashioned motels are fun, a couple of fancy places are good, and a bit of chill out AirBnBs with a pool when you fancy a break from too much doing stuff.
I'm generally not a huge fan of The States tbh, but, blimey, that as a good trip, you'll enjoy.