What kind of car(s) will you have access to? That will play a role in narrowing down which areas you can realistically explore.
The vast majority of the areas mentioned can be accessed with a non-4WD car. The western side of Canyonlands, though - the area called The Maze - is not something I'd dare to do without a 4WD and a lot of faith in my friends' navigation skills both on road and on trail. And if you don't have 4WD, accessing the east/north side of Canyonlands (and Arches) can be a very long drive.
The following is all stuff you can do without a 4WD:
Since Grand Canyon is by far the most difficult to visit in terms of permits, I'd maybe start the trip there. Get your lodging/camping/b-pack permits well in advance (which could mean NOW). If you want to b-pack but the others don't, maybe plan for 3 days/2 nights in GCNP with them camping and you hiking a 3-day route such as the Boucher/Hermit loop into the canyon? Just an example.
Vegas is maybe the best place to meet up if some of you have to fly in; it's cheap to fly there. Also cheap to rent cars there. Albuquerque or Flagstaff are other good places to start a loop; but tend to be more $$$ to fly into.
Suppose you start in Vegas. GCNP is a few hours' drive. After doing GCNP you could describe a loop north towards and through southern Utah, starting with visits to Monument Valley and Arizona's famous Antelope slot canyon, and ultimately ending with Zion NP which will get you to within 2:30-3 hours from your Vegas start/end point.
If, again, you want to b-pack while your friends just dork around and do day-hikes, Moab, Escalante River, and Zion are probably the 3 best destinations in Utah that accommodate both.
Of the places I mentioned before: (Utah roughly east-to-west)
Grand Gulch is not a good place to combine a b-pack with friends doing a day trip. They won't be able to see much in one day, whereas you'd need 3-4 days for a good b-pack to traverse the canyon.
Moab is a good base from which your friends can see eastern Canyonlands and Arches over several days. This is also a mountain-bike mecca. If you want to b-pack here, I'd pick the Needles section of Canyonlands. Or, just stick with your friends and get them to day-hike with you there, and go see Arches etc. with them, so you don't miss anything.
Capitol Reef NP is worth a drive-thru/stopover/camping for all of you.
The road from Capitol Reef to Escalante via Boulder has some of the most stunning views in America.
Escalante River drainage is an extraordinary and remote place, mostly known for its slot canyons. Your friends could do day-hikes to the main slot canyons, Lower Calf Creek Falls, etc. etc. while you either join them, or do a 2-3 day down Coyote Gulch and back.
Paria/Buckskin Gulch is maybe the best slot-canyon backpacking trip in America, but I'm not sure there is much for day-trippers in that area for your friends. Maybe others here will weigh in? For a b-pack trip you'd go in Buckskin and out Paria, that's 2-3 days.
Bryce NP is amazing and really small. Most people just hike 1-2 dayhike loops and then drive onwards. Or just car-camp one night. I did not really enjoy a b-pack trip here very much, as you can't b-pack the best parts of the park.
Zion NP has world-class backpacking (the Zion Narrows and the Zion Traverse being only 2 examples). Also lots to do for day-trippers, for a few days. Try to plan for several days there! (I b-packed Zion with just a walk-up, but that was years ago and may have changed...you may need reservations now.)
This is not even to mention some of the lesser known but amazing places in southern Utah such as Natural Bridges, Fish and Owl Creeks, Goblin Valley, Little Wild Horse Canyon, Rainbow Bridge, the Dirty Devil River, the Waterpocket Fold.
If I could only backpack two of the above mentioned places, Grand Canyon and Zion would be my choices without a doubt.
So my biased opinion is to cut Death Valley, Sedona, and New Mexico from your trip. (Okay, so if I had to add anything back in, it would be Canyon de Chelly and environs in far NW New Mexico.) You did not say how many weeks you will have. With, say, 3 weeks, the driving loop I described above is already PLENTY of driving - remember how huge the West is! You and your companions will probably feel rushed just trying to see this much of Utah, it is that extraordinary.