I spent 2 days in Iquique in June 1999 as a stopover on the way from Easter Island to La Paz. I really didn't find it very interesting or scenic and there was little to do. The waterfront does have a casino, a few highrise condos, and some OK seafood restaurants and there is a duty-free shopping area which is publicized a lot, but in my opinion is a complete waste of time (I certainly did not see any bargains). Perhaps there are some interesting sights out in the desert nearby (We wanted to see the Giant of the Atacama, but did not have time), but as for the city itself, I would either skip it outright or allow one day maximum there. Although I have not been to Arica, I have not heard many good things about it either.
If you have not yet been to the Lake District and Isla de Chiloe, that is far more scenic and interesting in my opinion.