If you want to stay in Flagstaff, do consider Bonito National Forest Campground at the entrance to Sunset Crater Nat'l Monument. It's a favorite place of ours - flush toilets, paved sites but no water fill or dump so come prepared. It's a lovely spot and is just north of Flagstaff on Hwy 89. Take the Sunset Crater loop drive with some awesome Indian ruins to visit.
From there head further north on 89 and pick up Hwy 64 west which will take you to Grand Canyon a scenic route. Since you're short on time and it sounds like you would be satisfied with a day at Grand Canyon, and that's fine. You can always come back for more. At the Canyon, park your car and hop on the free shuttle bus to tour the Rim. You can get on and off wherever and whenever you want. Do stroll the Rim Trail enroute. It's easy paved walking with great views of the Canyon.
Near the intersection of 89/64 stop at Cameron Trading Post for awesome Indian Tacos and a very high quality gift shop.
Walnut Canyon Nat'l Mon. is a little east of Flagstaff. South of Flagstaff in the Morman Lake area which is a nice scenic drive. Southeast you could do a day trip to Sedona via Hwy 89. Also, like you stated, just doing some Jeepin' around Flagstaff will give you some nice views, especially if you get up the mountain. Your three days will go by fast. Have a good one!