One minute you're staring at the willy-nilly sprawl of Apache Junction, the next you're so isolated and lost in time you feel in danger from Apache warriors. From Peralta Trailhead, you can either head to the right on the Dutchman Trail or left up through the steep-walled Peralta Canyon to the Fremont Saddle. It's about four hours up and back, which gives you plenty of time to forget the city. The trailhead sees fairly heavy traffic on the weekends from October to April, but is often deserted throughout the summer months.
The trailhead is so isolated, though, that casual hikers should bring a hiking buddy. And wear your heavier-soled boots. The sharp rocks will quickly bruise your feet in weak shoes. And, of course, bring plenty of water.
An even quicker alternative may be to start from the First Water Trailhead six miles east of Apache Junction on Highway 88. The dirt road from Highway 88 to the trailhead is only two miles long and the scenery is also spectacular, with a great view of Weaver's Needle. You can take either the Second Water Trail or the much longer Dutchman Trail, which connects on the other side of the Superstitions with the Peralta Trailhead.
(Directions: Take U.S. 60 east to Gold Canyon and continue east until you see the brown National Forest sign for Peralta. From the highway, it's seven miles on a sometimes-washboarded dirt road. Four-wheel drive is recommended but not necessary.)