Iglesia de San Francisco (Zela 103, tel. 054/22-3048, 7–9 a.m. and 4–8 p.m. Mon.–Sat., 10 a.m.–noon Sun.) is a 16th-century Franciscan church with a Latin cross shape and an unusual brick entranceway. The next-door convent, also designed in 1569 by Gaspar Báez, is worth visiting if it’s open, as is the adjacent Chapel of the Third Order, built in 1777.
Other convents and churches worth visiting include Santo Domingo (corner of Santo Domingo and Piérola, tel. 054/21-3511, 7 a.m.–noon and 3–7:30 p.m. Mon.–Fri., 7–9:30 a.m. and 3–7:30 p.m. Sat., 5:30 a.m.–12:30 p.m. and 6:30–7:30 p.m. Sun.), which was built around 1680 and has the oldest mestizo-style facade in Arequipa [1].
Another fine mestizo facade is to be found at San Agustín (corner of San Agustín and Sucre, tel. 054/20-0066, 7–9 a.m. and 4–8 p.m. Mon.–Sat., 7 a.m.–12:30 p.m. and 6–8 p.m. Sun.), for which construction began in 1576.
La Merced (third block of La Merced, tel. 054/21-3233, 6:30–9:30 a.m. and 4–8 p.m. Mon.–Sat., 6:30 a.m.–8 p.m. Sun.) has fine carved wooden sculptures and a colonial library.
La Recoleta (Recoleta 117, tel. 054/27-0966, 9 a.m.–noon and 3–5 p.m. Mon.–Sat., US$1.50) is a Franciscan convent built in 1648 with beautiful cloisters, a library, and a museum of Amazon artifacts collected by missionaries. It is located across the Río Chili, about a 10-minute walk east from the Plaza de Armas [2].
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/arequipa/sights/plaza-de-armas