The areas around Arequipa [1], such as Colca Canyon [2], offer fabulous trekking for those who like views of canyons and volcanoes and a hot, sunny climate. Unlike in the more popular Cordillera Blanca [3], trekkers have no problem getting off the beaten path and need not worry much about robbery or other safety issues.
The views range from immense canyon rims to wide valleys studded with volcanoes. The villages, isolated during centuries, are friendly and unforgettable.
Zárate Expeditions (Santa Catalina 115A, Window B, tel. 054/20-6314 or 054/997-1535), Naturaleza Activa (Santa Catalina 211, tel. 054/959-822-436 or 958-681-486, naturactiva [at] yahoo [dot] com), and Colca Trek (Jerusalén 401-B, www.colcatrek.com.pe [4]) offer the best organized treks and are glad to answer questions for those going on their own. Additional information about each of these agencies is available in the Climbing [5] section.
Topographical maps can be bought at the South American Explorers clubhouses in Cusco [6] and Lima [7], or the Instituto Geográfico Militar in Lima (or, in a pinch, copied in Arequipa).
If you're going on your own, remember to ask for detailed information—especially concerning the availability of water—at each village you pass.
Apart from running out of water, the main things to watch for are sunburn and getting cold at night. Bring a wide-brimmed hat, sunscreen for the day, a warm sleeping bag, and a jacket.
Links:
[1] http://www.moon.com/destinations/peru/lake-titicaca-and-canyon-country/arequipa
[2] http://www.moon.com/destinations/peru/lake-titicaca-and-canyon-country/colca-canyon
[3] http://www.moon.com/destinations/peru/huaraz-and-the-cordillera-blanca/trekking-the-andes/cordillera-blanca
[4] http://www.colcatrek.com.pe
[5] http://www.moon.com/destinations/peru/lake-titicaca-and-canyon-country/arequipa/recreation/climbing
[6] http://www.moon.com/destinations/peru/cusco
[7] http://www.moon.com/destinations/peru/lima