I think you need to focus on one area or the other. Bryce, Zion & the Grand Canyon (the circle tour) would be my pick. I'd add Antelope Slot Canyon, Horseshoe Bend, and others that JimMIA mentioned. My first choice is always to spend the night IN the park, and reservations fill up fast.
That would be a great 10-day trip if you carried it out a bit East from Lake Powell and hit Monument Valley (another Navajo Nation Park). You've seen all the car commercials, but it really is beautiful. We stayed at The View hotel right on the rim of the valley and the view was indescribable.
I'd fly into Vegas and go Zion, Bryce, North Rim of GRCA, Arches if it's not too far out of the way, the Page area including LOWER Antelope Canyon, then out to Monument Valley, back to Sedona, then South Rim GRCA, then back to Vegas.
But if I only could do ONE trip (and Yosemite wasn't involved), I would fly to Jackson and
really explore Yellowstone, Grand Teton, and Jackson itself.
Grand Teton is just breathtaking scenery + some early settlements. The "Cathedral View" from Cunningham Cabin and the church is beautiful. Lake Jackson and Jenny Lake have huge mountains rising right out of the lakes.
You'll also see some cool wildlife at GRTE, but Yellowstone is the place for megafauna -- all of the big guys, and they're not hard to find. Plus a beautiful canyon, a great river, thermal features beyond description, a majestic lake...what's not to like.
And don't discount Jackson itself. Just outside Jackson is the National Elk Refuge and Jackson has a lot of old cowboy charm. There are raft trips, and horseback riding -- all kinds of memories to make.
