On my way from the south of California to near El Paso (Texas), I visited several deserts (Joshua Tree in California, Arizona Saguaro, ....). This park is in southern Arizona, near the Mexican border, with police checkpoints every few km. It's well worth a visit, though! From the visitor center, about 20 km from the park entrance, there is a list of possible routes depending on how long you'll be in the park. The one I recommend is a route by car, on unpaved road, about 30 km upon leaving the visitor center. On the same route you can try some trekking, usually to the most photographed arch of the park (the road doesn't get to the base).
I went through this town because I wanted to visit Organ Pipe Cactus Park. The truth is that neither one of us knew of its existence. But I liked it, its fine architecture, its main square, its mine, which is still in use, along with that is the people in the area. It's a must-see if you travel these deserted border lands in Mexico.