Iquique is one of the driest places on earth — measurable rainfall in a year is rare — and it has 300-plus days of sunshine. The weather is therefore not really the question; what matters is when you want to share the city with crowds.
The Chilean summer holidays (mid-December to late February) bring a surge of domestic tourists, and the beachfront fills up. Prices for accommodation rise sharply. The shoulder months of March, April, October, and November are the sweet spot: warm enough for the beach (water temperatures in the high teens), uncrowded, and easier on the wallet. Winter (June to August) is mild and sunny by day, but the evenings get cool and a coastal fog called the camanchaca can hang over the city in the morning.
The Festival de La Tirana in mid-July, an enormous religious folk festival 70 kilometres inland, is a major regional event worth timing a visit around if you can.