October is a great time to visit the southwest. No summer crowds.
Don't miss the Grand Canyon, if you have never been there. The more time you spend there, the more you discover. We spent two weeks there last summer. There are many hikes down into the canyon. The one I've done was three days- Day 1: down the Hermit Trail, Day 2- across the Tonto plateau to Indian Gardens, Day 3 up the Bright Angel Trail to the south rim. You can leave your car at the south rim and take the tram to the trailhead for the Hermit trail, so it makes the car logistics easy. I did this hike in late April so the temperature at the bottom was not too crazy. Advance reservations are needed.
Another cool hike is the one to the Navajo National Monument (about 8 miles each way) and you can camp up there. You can also do it as a day hike. You need to make reservations in advance. You will see things there you cannot see anywhere else.
Bryce and Zion also offer a lot of opportunities.