Having visited the Grand Canyon recently, you'd be surprised at how much there is to see, since there are two very distinct areas...the North Rim and the South Rim.
We started with the North Rim, staying inside the park at the CG there. It's far less crowded than the South Rim, and since it's at a higher elevation, the weather is cooler. Somewhat like a USFS CG, there's all sorts of opportunities there. A short hike from the CG to the Lodge provides all sorts of vistas of the canyon, and once you get to the Lodge, the views are even more spectacular. There's several hikes in the immediate area of the Lodge, and drives to several other points of interest on the North Rim also provide a unique perspective of the canyon.
Family members did the hike from the North Rim to the South Rim. 27.3 miles IIRC. Somewhat strenuous hike down (the longer part), and stay at the Phantom Ranch on the Colorado River, and then a hike out on the Bright Angel Trail on the South Rim. For those family members, that was a solid 2 days; with the right reservations, one can make it a long longer in the base of the canyon.
As they were hiking, I was moving the trailer around to the South Rim. Stayed at Trailer Village with FHU, quite different from the North Rim. And the South Rim is busy. Even in October, it was still heavy with tourists, many from other countries. There's 3 very distinct areas to explore at the South Rim, and each can take a goodly part of a day. There's also an excellent transportation system there, to get from point-to-point. If you decide to do both rims, a week would be a good amount of time for both sides.
Beyond The Grand Canyon, there's the "Big 5" in southern Utah. I'll defer to others who have been there (since I have not) to give you info on them, but I will say that, with the choices of the Big 5, you will be able to fill 5 weeks (4 weeks actually, given your travels back/forth). One site that was interesting in getting to the North Rim is the Najavo Bridge on US 89A. Great place for a break from travelling, and some fascinating information on the area surrounding the Bridge.
Whatever you decide, hope you have a safe and memory filled trip!