Irene,

It'll be tricky to find things going on outside of the big 4: Phoenix, Tucson, Flagstaff, Prescott (in descending order of size), which is not to say there isn't anything. In fact, I'm thinking that just recently I was surprised to see a note of someone recognizable performing in Safford, but not elsewhere... I'll see if I can dredge that up.

On the reservations there's likely to be even less of "unaccompanied contemporary folk", although bluegrass is a good bet.

...

I've retrieved the Safford event: Footworks Percussive Dance Ensemble is going to be there next week. That doesn't help you, but they're being presented by the Gila Valley Arts Council, who have a schedule of other events.

This is a link to a pdf list of local Arizona arts agencies from the Arizona Commission on the Arts. That might get you to similar events in out of the way places, since Arts Commission funding helps the smaller communities bring artists in.

I originally found the Footworks event on the KXCI (Tucson community radio) web site. I'm not sure why they're listing things quite so far afield, but what the heck. They don't have any April events listed yet, but you can check there closer to your visit. KXCI Events Calendar.

Hope this helps!

~ Becky in Morristown (for now)