Zion - Bryce - Page - Grand Canyon Itinerary

You're last drive from the Grand Canyon back to Las Vegas will be the longest at around 5 hours. The rest will be three hours or less unless you make stops. I like doing the route in reverse for a few reasons. You get the longest drive out of the way, you have really spectacular views as you exit the Grand Canyon over looking painted deserts as you descend towards Cameron, AZ. As you near Lake Powell, you again have great views as you descend towards Page. Then by doing Zion last, IMHO, you've saved the best for last!

Everyone has the favorites as far as the N. Rim vs the S. Rim. The N. Rim is a 1000 feet higher in elevation and will be cooler and less crowded. I personally like the S. Rim because there are more overlooks and to me they are grander. I always recommend first timers to the Grand Canyon see the S. Rim first...but that's just my opinion.

By staying in Zion you are in the canyon and have fantastic views, but Springdale, Utah is almost as good because you are at the gateway to the park with great views and the town has free shuttles to the park entrance where you can then pick up the free Zion shuttle. Bryce you can't see the canyon from the lodge, but it's just a short walk to the rim. If you stay just outside the park at Ruby's Inn, you can pick up the free Bryce shuttles to go into the park.

About the ski boat rental at Lake Powell. If you do rent a boat buy a good map of the lake, it's easy to get lost!!!! If the main channel isn't open because of low lake levels, then I will warn you that the Antelope channel is a 12 mile, deep and narrow that is really rough water. It will take you all day to get to Rainbow Bridge and back but it is fun exploring the lake. If they have boat rentals at Antelope Marina...get them there!!!! It will save you most of bad area of the channel!

Utahtea

Other than the boating, I did the same trip last summer and loved it. We preferred the north rim because we didn't want to deal with hoards of people in a setting like that, but I do suspect the south rim may have better views (if for no other reason than that you are looking north not south). My trip report describes all those places, the drives between them, hotels,etc.
http://www.fodors.com/community/united-states/water-in-the-desert-the-great-southwest-national-parks-trip.cfm

I totally agree with Utahtea and will add that as for lodging at GC, the view is down, not up so mostly you don't have the view from the lodging choices. For the north rim, the in park choices are all there is close by. The south rim has in park lodging "on the rim" : el Tovar, Bright Angel, Thunderbird and Kachina, and back a bit Yavapai and Maswick. If you are planning for this year make reservations now for which ever rim you choose and if they say they are full, call and keep calling as people make reservations a year ahead and then cancel as time gets close.

At the Grand Canyon, do hike down into the canyon a bit as most of the "crowd" is at the top. Staying in the park also means that the day trippers will not be there in the early morning or evening, the nicest times there IMO.

In Page, look into the half day smooth water raft trip down the Colorado river from the dam to Lee's Ferry, as well as Antelope Canyon (off rt 89 not the water one) and Horseshoe Bend overlook.

Have a wonderful trip.

I think Utahtea and Emalloy have already given you some valuable advises. I just want to add few things. I have done this loop in both directions, and I think doing zion/bryce/page first is better. I personally felt that after seeing grand-canyon, I didn’t enjoy Zion as much as I could have otherwise! But I agree that GC to Las Vegas is a long drive, so plan accordingly if you keep it at the last.
Zion is ok if you don’t stay in-park. They have very nice shuttle system. You could do some small hikes like emerald pools, river walk, weeping rock etc. (visit NPS website for details)
If you have only 1 night and if you could manage reservation, try to stay in-park at Bryce. The sunrise time is awesome, and sun rises very early in the summer
At Page, don’t miss sunrise at Horseshoe view point near Page, and also the Antelop canyons (~1-2 hrs). Rainbow Bridge is really big and stunning. We also like Mexican dinner at Fiesta Mexicana (I think that was the name…)
At GC, I would advice South Rim. Yes, it has more view points, more options for small hiking and more in-park lodging – but still its hard to get a room in the summer. So book a room now, it’s refundable For hiking options, again check NPS website.
July would be pretty hot, but not impossible in this region. If have enough time on last day at Las Vegas, make this loop as you planned originally. (Zion first and so on…)
Have a wonderful trip!!

I have not done Canyoneering in Zion, but have in Moatwice). Since you mentioned it-THEN DO IT. The very best adventuring we have ever done.
Don't miss--
Angels Landing in Zion-do it early to avoid the heat
The Narrows-rent your gear at Zion Adventure Company, they also would probably be your best bet for guides for canyoneering.
At Bryce--Navajo Loop/Queens Garden hike, Ranger-Led Night Sky, Horseback riding on Peekabo Loop

For us, we alway prefer staying "in park". We really enjoy the historic old lodges. Yes they are a premium price for what you get. I do see how they might not be for everyone. I think at the GC you certainly will need to stay in park as there really isn't any other choice. Depending on what you want to do at the GC, maybe just one night there would be enough. In July the North Rim would be the cooler option. Bryce will probably be ok temp wise. Zion will most likely be warm or hot. Do The Narrows in the middle of the day to stay cool.

Actually, in July, you might not need to rent much gear to hike The Narrows. I would probably just rent the shoes and just go in shorts. You will want a hiking stick for this trek. I never have one on hikes, but they certainly help a lot on this hike.