I highly recommend a half or full day float trip in Glen Canyon, up by Page, AZ (I guided on those trips for 8 years). 15 miles of flat water rafting in an amazing canyon. The only way you could pick up a Grand Canyon whitewater rafting trip in October is to get in on a cancellation for a full oar trip (14 days) or half oar trip (6-8 days). I guided on those trips too, here is a site with all the outfitters; I worked for Wilderness River Adventures. To do the float trip, you can either drive up to Page (about 3 hours from Williams) or book a trip that leaves and goes back to the South Rim of the Grand Canyon.
If you chose to go up to Page to do the flat water trip, you can also do lots around that area. Hike Antelope Canyon, or contact Lake Powell Adventure in Page (owned and operated by a fantastic gal I guided with in the Grand Canyon). They conduct bike tours and four-wheel drive tours around the Page area, and kayaking trips on Lake Powell in the side canyons.
Around Flagstaff, you can visit the Lava Tubes, head down I-17 a bit to Montezuma Castle, and lots of good food in the downtown area.
Up at the South Rim of the Canyon, visit the Kolb Studio. You can hike into the Canyon but wear good hiking shoes and bring water (even in the fall). You can go down half-way to Indian Springs, which is about 4 miles. Just remember you have to hike out!
And don't forget you can always visit Prairie Dog Flats and see if our favorite plygs are building their ginormous homage to Kody!