Alaska Mike is quite correct in recomending Chinle, that is the entrance to Canyon De Chelly, an amazing place and well worth adding to your itinerary. However, the interstate that takes you through Flagstaff is "I-40" not "I-10", the latter does not go north of Phoenix. I-40 is what remains of old Route 66.

With Meteor Crater to the west, Canyon De Chelly to the north and Petrified Forrest National Park to the east, Holbrook winds up the center of a wonderful adventure. You could go south into the high pine-covered mountains, but June or later would be better than April.