The standout day (or rather, overnight) trip from Arequipa is Colca Canyon, four hours north-west of the city by road, one of the deepest canyons in the world and the best place in Peru to see the Andean condor. The standard package is two days, one night, with an early-morning visit to the Cruz del Cóndor viewpoint and a stop at the hot springs of Chivay on the way back. Single-day trips technically exist but involve so much driving that they aren't worth the time.
Shorter trips from the city: the colonial mill at Sabandía, the Inca terraces at Yumina, and the pre-Inca petroglyphs at Toro Muerto (a long day, three hours by car). The latter is one of the largest petroglyph fields in the Americas — thousands of volcanic stones carved with humans, llamas, dancers, and abstract motifs by the Wari and later cultures over a span of nearly a thousand years.
