We spent an entire morning wandering around the Monastario de Santa Catalina in Arequipa, so picturesque - I loved the bright colors, the red geraniums everywhere, portraits of dead nuns (apparently they're only allowed to be depicted after death), views of Arequipa's mountains and volcanoes, honeysuckle...
Paintings of Saint Jerome and Saint Christopher became our favorites to see throughout the trip, they almost became like old friends.
I would highly, highly, highly recommend making time to explore it.
Another really good stop in Arequipa is the Museo Santuarios Andinos where you can see the incredibly well-preserved body of "Juanita," the first of fourteen Incan child sacrifices to be found in the mountains of South America.