My recomendation is to stay at the Grand Canyon. For me, it's all about seeing the way the light changes the canyon during the day and evening. Sunset and sunrise are spectacular--and very inconvient to see if you are staying elsewhere. For me, because I don't hike--and because it's easy to go from the Phoenix area--getting to the canyon about noon and staying overnight (preferably with dinner at El Tovar) so I can walk along the rim in the afternoon and see the sunset with the bats flying up out of the canyon and then getting up the next morning for sunrise are what make the trip. On "the sunrise day" you still have the option of spending almost the whole day along the rim if you want. Hikers and mule tripers, of course, need more time. For me, the drive consumes too much of the day to do any more than required, so I would never consider staying in Flagstaff and driving up and back several times. You would catch the canyon at the same time of day each trip, and I think you'd wind up saying "Do we really need to go back?"
I like staying at Kachina rather than at El Tovar (and I've stayed at El Tovar 3 times). Kachina is more modern, though a bit Super 8ish. However, it's charm, for me, comes from the fact that it's built facing the canyon, so half the rooms actually overlook the canyon. El Tovar is built with "the narrow end" facing the canyon, so very few rooms actually overlook it. Some of the rooms are nice, some are mediocre, and some are truly horrible. I've stayed in a truly horrible one and 2 mediocre ones; I've never stayed in a suite. At El Tovar, you have almost no choice because of the crowds wanting to book--I would never have voluntarily taken the basement room that was truly horrible, but when you check in, you get what you get, and if you don't want it, the guy behind you who doesn't have a reservation will take it With Kachina, you can book canyon side or parking lot side.
If you decide to have dinner at El Tovar, book a reservation as soon as you know your date. The reservation desk has a sunset calendar right by the phone and they will work with you around sunset. One time we were there and eating when it was sunset. They went through the dining room with a chime/ceased serving/and allowed all of us to go out for sunset and then return to continue our meal. Generally, they book you before/after sunset, though.
On the way to the Grand Canyon, you might consider making time for Canyon de Chelly
http://www.nps.gov/cach/index.htm It, too, is spectacular and it's totally different from The Grand Canyon.
If it were me planning the trip, I'd go to the Grand Canyon (and Canyon de Chelly) before going to Flagstaff or Sedona. And, again, if it were me, I'd never choose Flagstaff over Sedona. If you decide to do the day trip to the canyon, the drive from Sedona is only about 30-40 minutes longer than driving from Flagstaff, and you'd have the advantage of being in Sedona, not Flagstaff. Flagstaff is nice enough, but it really isn't all that special, and Sedona is special and unique.
Make time for some Native American ruins while you're there, too!
