I think the city centre of Arequipa must be my favourite old town in Latin America (or at least joint with Havana!). The Unesco world heritage site is a series of beautifully maintained streets with white stone Baroque buildings all with facades of intricate carvings that give you the feeling of being in a different time and world. The low rise nature of the buildings (almost all are only 2 stories tall to protect from earthquakes) add to this vibe, and so do the three majestic, dramatic, perfectly coned volcanoes that surround the city off in the distance.
On top of that, the food is superb and its a great starting point for a 3/4 day adventure for Hiking and zip-lining in the Colca Canyon.
A must visit for Peru, along with the adventures near Cusco area (see entries for more details on these – Machu Picchu, Hiking the 4 day / 3 night Inca Trail, Driving through the Sacred Valley, A walk around some of the key Inca sites near Cusco).