El Wagon
Thompson 85, +56 57 411647. outstanding and generous seafood. a bit more expensive than other places but it's worth it.
Al filo D'Oro
Pizzeria Al filo D'Oro, O'Higgins 964, +56 57 42 04 18. Thick crust pizzas for Ch$ 5000 and up. Pleasant spot with outdoor seating.
Iquique's Chinese inmigrants that arrived during the 19th century as slaves to work in saltpetre extraction, have had a distinct influence on the local food. The area around the mercado is Iquique's Chinatown. You'll find a large number of Peruvian influenced "Chifa" restaurants here, all pretty expensive. The smaller restaurants between them are cheaper, and serve sandwiches and burgers for Ch$800 and up. McDonald's, Domino's, KFC, and other fast food chains can be found in malls.
For dessert you can try the chumbeque invented by chinese descendants. It's prepared with layers of fried thin dough filled with different fruity caramels. Nearby towns in Iquique specially Pica and Matilla offer a variety of fruits and desserts made with them, the best known are the alfajores.