Hank,
We took a day trip to Safford while visiting friends in the Willcox area -- although we haven't stayed at either place, we brought back info for 2 Safford campgrounds.
Roper Lake State Park: a small SP but very nice & some sites looking out over the lake; and they have a natural spring 'hot tub'. We were told the park fills up quickly!! This would be our first choice.
http://azstateparks.com/Parks/ROLA/index.html
Golf Course Road RV: at the time, it was still fairly new, but quite honestly what I remember most was very close quarters, concrete pads, no grass & no shade.
I also made a note that there's a WalMart Supercenter in town
Simply as an FYI... (waaaay east of Safford) on US Hwy 191 near Morenci there's a low (12'10") bridge/tunnel at mile point 169.90. You probably won't be towing in this area, but be aware just in case.
ON EDIT: Golf Course Road RV is apparently under new management... see reviews!
http://campgroundreviews.com/regions/Arizona/Safford.html
Hope this helps,
Terri, the Chevy co-pilot