The peaceful neighborhood of Yanahuara makes a diverting excursion from the city center. It's within walking distance: go west on Av Puente Grau over the Puente Grau bridge, and continue on Av Ejército for half a dozen blocks. Turn right on Av Lima and walk five blocks to a small plaza. At the side of the plaza there's a mirador (lookout) with excellent views of Arequipa and El Misti.
The round-trip walk from the city center should take around two hours, but there are also combis (minibuses) to Yanahuara from along Av Puente Grau (and returning from Yanahuara's plaza to the city) every few minutes to speed you along.