Flagstaff is one of our favorite places is stay .... because it's a friendly, low-key town. We always stay at Bonito National Forest campground which is a beauty.
OP: You said you're only spending a night...and that you're touring Grand Canyon. I would highly recommend that you spend at least 2-3 night at the Grand Canyon. The park has very nice campgrounds - dry and full service right at the canyon's edge. There is also Ten-X national forest campground just outside the park entrance. Why stay in Flagstaff?