Arequipa is a pleasant enough city and I enjoyed my stay there, but it didn't seem particularly outstanding to me.  The main square and cathedral are quite nice, and there are a couple nice small museums featuring Andean mummies.  I think the volcano connection makes it a little special -- the city has grand views of multiple snow-capped volcanos, and the signature white buildings are made from pyroclastic stone. This is the first place where I was aware of that being used as a building material. 

There are a variety of "free" walking tours around town.  Most of the people I talked to didn't have great recommendations of the one they had taken, and I was disappointed in the one I joined also, but it did lead me to a couple interesting courtyards (upper right photo) and spots that I wouldn't have found on my own.

The description here mentions that local building "designs show the integration of European and native" and I noticed this in the unique carvings on the church at the Yanahuara scenic overlook (photos).

Arequipa is a good place to take a breather on a trip through Peru.  I enjoyed nearby local attractions. I used Arequipa as the starting place for my Colca Canyon overnight trek, which was an intense day of hiking but very rewarding (and also not particularly close to Arequipa). Closer to town, I took the popular half day tour to the Ruta del Sillar, which takes you the quarry of the city's signature stone, which now functions as a kitschy sculpture park.  The second half of the tour goes to Quebrada de Culebrillas and I enjoyed it a lot more.  Culebrillas is a natural canyon cut through the stone which leads to some petroglyphs.  The canyon reminded me of a miniature version of Petra's Siq.