I wouldn't recommend driving to Quartzsite for your 'experience' in March. Most of the action would be over and it would be getting hot. Since you're heading back to Illinois, I assume, then pick somewhere else.
Roosevelt Lake at the Cholla campground would be an excellent choice at that time of year. It's not exactly boondocking but it's dry camping. From Phoenix you'd take 60 to Globe and then pick up 188 to Roosevelt. Windy Hill campground is also nice with options for electric. Both are Tonto national forest campgrounds.
You could also take 87 to Payson and take 260 over toward Show Low. There are many beautiful national forest campground right along the highway.
On Hwy 89 just north of Flagstaff is Bonito national forest campground at the entrance to Sunset Crater Nat'l Monument. It's a beauty and you'd be ready to head east on I-40 toward home.
Also just south of Flagstaff around Mormon Lake are some nice national forest areas - some just plain boondocking and there is Pine Grove national forest campground.
Have a great time!