I'll assume those citing Moab are really referring to CanyonlandsNP, JFYI, Moab is a cool town but a few hours is more than enough, unless you want to shop.
I would hold off and save Arches for another trip. There is a lot of work going on in ANP, road work, parking areas, and waits and blockages are going to happen.
I would split the Utah adventure into at least three areas, North of Moab, Arches, Island in the Sky, Dead Horse Point and the other areas near there. North of that would be Bryce and Zion NPs. And the immediate area South of Moab as far say as a drive by at Medicine Hat, but include The Needles District of Canyonlands, Muley Point, Natural Bridges, Goosenecks, Mokey Dugway and Valley of the Gods.
The State of Utah will send you information on all those areas and if you are a AAA member, they have some great maps and Tour Books. Also visit the National Parks website for Parks information.
As far as the GCNP, there is so much to see, do and learn in the developed area alone that several days would not be enough. The Ranger programs are unbelievable, the NP Visitors Center is fascinating, WALK of Time(or Ages), along the rim gives you a sense of the content of the various geologic layers of the canyon and the time frame of the creation of the Canyon.
The First Nations People are returning to the Canyon and they have demonstrations of their rituals and dances that are held near the Trading Post, there are demonstrations of their arts and crafts, daily life and history in the facilities surrounding the new restored Watch Tower.
The vistas of course are remarkable but don't be a ten minute tourist. The things I have mentioned are within walking or shuttle distance and in the case of the Watch Tower a very short drive. To me and my DW those man made things that are must see are the Coulter fireplace in the hotel, the Trading Post, the Kolbe Studio and home, the Watch Tower was also designed by Coulter and Hermits Rest, also Coulter.
A natural event if you are lucky enough to be caught in it is a monsoonal weather cell. The lightning and the rain in those cells are fantastic. There is all this and there is the unbelievable experience of hiking or riding a mule to the bottom of the Canyon.
And don't forget the ice cream at the hotel gedunk stand.