@great_lakes_mom has great advice. North rim or south rim, stay inside the park for the best experience, do some hiking, and definitely watch the sunrise and sunset.
In the Flagstaff area, our family favorites are Sunset Crater and Wupatki (get the national parks pass if you’re seeing those and the Grand Canyon), the Red Mountain Trail (we all loved this), the Lava River cave if it’s open, taking the ski lift to the top of Mt Humphreys, and the Old Caves Crater trail which is right near Flagstaff. We’ve also had fun at the Grand Canyon Deer Farm near Williams and a lot of people like Bearizona.
In Flagstaff we like to eat at the Beaver Street Brewery or Diablo Burger and get coffee at Macy’s.
Near Sedona we like the West fork Trail on Oak creek canyon.
In Phoenix in May, wake up early and go to the Desert Botanical garden or do a hike first thing in the morning for nice weather. Then go to a museum or shopping in the afternoon. We love the Musical Instrument Museum.
With regards to driving, there’s just a lot more open space out here than the east coast. Fill up your car with gas before leaving any city. Carry water and drink a lot of it. It’s dry here.
Arizona is a beautiful state and has a huge diversity of landscape and ecosystems. Our daughter and Her husband recently moved to Tucson and have been exploring the southern part of the state and there’s some incredible places. Chiricahua National Monument really should be a National park. But it’s more spread out and remote in southern Arizona and harder to see on a quick visit.