Arequipa is renowned for its succulent gastronomy. Its rich dishes are traditionally consumed in rustic restaurants with firewood cuisines known as Picanterías; that is, the place where picantes (or a spicy stew) are served.
Rocoto relleno, stuffed red hot peppers, is probably the most well-known recipe. Rocotos are stuffed with spiced beef or pork, onions, olives, and egg white, and then cooked in the oven with a sauce of cheese and milk.
Ocopa is another traditional dish. Similar to papas a la huancaína, ocopa is a starter consisting of yellow potatoes covered with a sauce of ajíes, walnuts, huacatay (a Peruvian herb that gives a vivid green color), and fresh cheese.
Chicharrones, deep-fried pork, is also a favourite, as well as the adobo, a a pork stew made with hot peppers, onions and chicha (a traditional purple-corn beer).
Arequipa is particularly appreciated for its great prawns, probably the finest is the country. These can be enjoyed simply grilled or in more elaborated preparations such as a picante, a chupe soup, or a locro (a spicy pumpkin stew).
Many good, inexpensive restaurants serving traditional fare can be found next to the Plaza de Armas, specially those located in the Santa Catalina and San Francisco streets. Two of the finest, however, are located on the outskirts and cab be reached with a short taxi ride.
La Lucila Sachaca is a picantería run for decades by Lucila Salas de Ballon. A short taxi ride out of town, this old style kitchen features cuy (Guinea Pigs) eating scraps in the corner, and Lucila still making her sauces the old way, while keeping an eye on everything and everyone.
Ary Quepay (054-672922) is a friendly, family-owned eatery serving local dishes, much appreciated by locals.
El Camaroncito (San José 103, Cerro Colorado, 054-255628) is a nice restaurant specializing in fresh-water prawns and shellfish.
Sol de Mayo (Jerusalén 207, Yanahuara, 054-254148) is probably the finest restaurant in the city. Located in the Yanahuara quarter, some 5 minutes in taxi from downtown, this elegant restaurant has been delighting Arequipeños for over a century with local specialities such as chicharrones, prawns dishes, and ocopa. Elegant but affordable.
Similar to Sol de Mayo is Tradición Arequipeña (Av. Dolores 111, Paucarpata, 054-426467), also located on the outskirts of the city, in the Paucarpata district. A lunch-only restaurant, its menu includes typical Peruvian recipes such as adobo, picante, and ceviche. Much appreciated by locals.
Govinda (Jerusalen 505, 054-285540), run by Hare Krishna, is a good option for vegetarians with inexpensive lunch menus (less than $2).
With excerpts from Wikipedia and PromPeru.