Off the beaten path
The only legal public access appears to be from Helvetia Road on the South side.
Houghton Private Access
The following crosses private land. Do not break the law. If you do not have permission then figure out a route from Helvetia Road.
This is the Northernmost peak of the Santa Rita Mts, Southeast of Tucson. I looked a long time exploring rough roads around the base by jeep and mountain bike, trying to find the closest starting point. Most of the land on the North side of the peak is private. The East side has very rough jeep trails that don't even get you that close. I then explored from the West and found a gravel road off of S. Houghton (S. of Corona De Tucson). I decided that enough was enough, this would be our starting point.
I rounded-up my hiking buddies and we set off. The hike is a scramble across numerous hills and valleys. You pass through a small forest of saguaros on the South face of one slope (rare to see at this altitude). Mt Fagan is sort of a double peak, with the lessor peak being to the West, this is what you're aiming at. We got on the shoulder of that Western peak and decided to skirt the top of it and traverse the North side. Once we were around that there was another false summit to traverse. We ended up on a saddle between this false peak and the main peak. It was one more scramble up to the actual summit. On top we had great views of the whole Tucson valley. I noticed to the South, there was another road at the base of the peak that may have gotten us closer, but the route would have been steeper.
This is a great seldom-climbed peak to do if your looking to get away from the crowds and do something "out there". Mt Fagan is 6189'. GPS showed our vertical gain of 2149. I'm unsure of the distance, but I would estimate 8-10 miles round trip. There is a SAHC register at the top.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.