I just got back from Arequipa. I had two lovely lunches there (late lunch is much more popular than dinner in Peru).
I would highly recommend either of these places. Both have very beautiful patios and specialize in Arequipa cuisine e.g. Chupe de Camorones and rocoto relleno.
Restaurant Sol de May, Jerusalen 207 near the district of Yanahuara.
Restaurant La Tradicion, Av Dolores 111
Also, if you need a place to stay, I stayed at a lovely bed and breakfast called La Casa de TinTin.