I agree that Flagstaff might be a good base; definitely the cooler of the Arizona options, and you could certainly do a day trip to the Grand Canyon from there. (An overnight at the GC is best, but might be more effort checking in/out of hotels with a large group.) There are a number of hotels, B&Bs, and cabins in Flag to choose from.
Here's another option, in case you're interested in Sedona. You could stay in Oak Creek Canyon, which is generally a bit cooler, but is only a few miles up the highway from Sedona. There's a place called Junipine Resort; it's a condo/townhouse type facility, located right next to Oak Creek among lots of trees. The units have multiple bedrooms and baths, plus full kitchen facilities. Some have hot tubs on the outdoor decks; the nicest condo locations are the ones right on the creek. I'm just thinking that it might be a good fit for your group; I've been there a number of times, and it's quiet and very relaxing, with plenty of space for groups and families to spread out.
The condos are all individually owned and decorated, and therefore some of them aren't the most "modern or up to date" furnishings, but they're definitely clean and comfortable. From Junipine, it's a beautiful drive up Oak Creek Canyon to Flagstaff (about 20 minutes), and a little more than an hour from there to the GC. You'd also, of course, have easy access to Sedona and all it has to offer.
Edited: 13 July 2012, 2:13