Just to follow up on joel's good suggestion for Wupatki, Sunset Crater National Monument is also very nearby, so you can hit them both.
One caution? Both of these are recommended stops along the way from Flagstaff or Sedona if entering Grand Canyon National Park park from the East Entrance (turning west on 64 off 89 at Cameron). You get a fantastic initial eyeful of it from the first overlook (Desert View.) Unfortunately, that entrance is closed due to troubling COVID numbers affecting the Navajo Nation and there's no indication when it will be open again. If it's still closed in October, your only access is via the South Entrance, just north of Tusayan.
A half day poking around funky 'ol Jerome can be a good time. :O)
Editing to add: about that train from Williams....
IMHO, I wouldn't recommend that one as a day trip. You can get to the canyon much faster with your own vehicle, stay much longer, and get home much quickly. That train takes 2 hrs, 15 minutes to cover the mere 65 miles to the park from Williams, the same on the return trip, the scenery en route is nothing to write home about, and you only get 3 hours to explore the park. You also won't be there when the light is at its best, which is darn near anytime but at the middle of the day. That's when you'd end up there if going by rail.
One more caution? Be very cautious if driving after dark in that part of the country; lots of wildlife out and about! That's just one of the reasons most of us recommend staying at least 1 night in the park. Plus you can enjoy a sunset, a sunrise, or both, if the skies cooperate. :O)