Most people who visit Arequipa take a tour out to the Colca Canyon, one of the worlds deepest canyons formed by an enormous seismic fault between the Coropuna (6425m) and Ampato (6325m) volcanoes. (actually the worlds deepest canyon is the nearby Cotahuasi Canyon).
The tour can be arranged on arrival in Arequipa at one of the several tour operators or travel agents around the Plaza. Many hotels can also arrange this activity. Although a tour can be fit into one day, it's best to go for at least 2 days, staying the night at the village of Chivay (3633m) the first village on the edge of the canyon.