I live in Arizona. Route 66 in Williams is interesting. Its only a few miles long but at night it kind of reminds me of something out of Cars. You could take the Grand Canyon railway from Williams to the Grand Canyon. I think they give you around 3 hours to explore the canyon and then you bring the train back. Its kind of a neat fun ride.
As for Sedona, I have a jeep and go there for a lot of the fun off-road trails. You could do a pink jeep tour. I would recommend one that does the broken arrow trail. It has some neat views and a fun trail exit that usually seems to scare the passengers lol. Also since youre going in the summer I would hit up slide rock state park. This can be very busy in the summer but its really fun and neat. As for horseback riding I cant really recommend anything since I have never done it. Also you should try the cowboy club. They have rattlesnake and cactus fries!
If It where me planning the trip, I would drive straight to Williams and do the canyon. Come back to flagstaff spend the night and explore sunset crater which is an old volcano that has lava tubes you can explore. I would also check out walnut canyon national park this was home to Native Americans who built cliff side dwellings. You can hike right into them. Then when I left flagstaff I would take the back way down to Sedona thru Oak Creek canyon via highway 89A. This will then bring you right into Sedona. The views and drive are very scenic. Then from Sedona I would either go to Jerome or maybe head back towards phoenix and visit Montezumas castle near Camp Verde. This is all assuming you will want to spend more time in the high country and not in the 115 degree heat lol.
