Sounds like a great trip! Since you've got a tight schedule, I'd take I-80 or I-70 to the Rockies to save time. Maybe even go south and take I-40 for a little Route 66 flavor. If you take I-70, I'd cut south at Limon, Colorado on US-24 to avoid Denver traffic. I-70 west of Denver is a beautiful drive but the traffic has become horrible. US-24 takes you to Colorado Springs and from there you have several great routes to the Grand Canyon.

It's hard to go wrong in southern Utah and northern Arizona. With so many great roads I'd take a different route home to make the trip even better.

As for hotels, if you decide to stay in Moab, Utah be prepared to spend a fortune. I stayed there in late October and paid well over $300 for a night in a Hampton Inn! The national parks in the area are spectacular but I've rarely seen such expensive hotels.