Iquique is one of the cheapest cities in Chile, so when you wanna go wherever you want just call by phone a taxi or catch one in the street. The cost must be similar and it is about (1,5 dollar) a ride to each point of the city.
But if you go with another person is better to call by phone because you will have to pay (1,5) anyway so is even cheaper.
There are several flights a day to Iquique departing from both, Arica and Santiago, Chile.
Departing from Santiago, the ticket is from USD120 roundtrip, but maybe yopu could get something cheapest if you find a last minute offer.
Also there are daily flights departing from La Pax, Bolivia.
Airlines operating Santiago - Iquique: LanChie, LanExpress, Sky Airline.
One way to get to Iquique from Arica, is by bus. It may not be glamorous, but it only costs 3000P/$5US per person (Nov '03). The trip took about 4 hours.
Our bus (Pullman Santa Rosa) had adequate leg room. The overhead was sufficiently large for our small backpacks, so we did not have to stow them in the luggage compartment. No food (normal), but we did get a cup of tea (not normal on most buses).
In the north of Chile, be prepared for a lot of police/customs checks. On this particular leg of our trip, we were offloaded and had our bags checked. More of a concern was when the bus steward took everyones I.D. including our passports, stuck them in his pocket and took them to the carabineros. It's bad enough when someone grabs your passport without explanation, but we were afraid our tourist cards (which were just loosely stuck into the passport) might be lost and then we would be in trouble. In future, I would keep the tourist document seperate from the passport.
As usual on a Chilian bus, be sure to bring water, snacks, toilet paper and sanitary hand wipes/hand towels. Even on long trips do not expect drinks, food or ANYTHING in the toilet except the toilet (which will be pretty filthy in a short time!) itself. Having said that, traveling by bus is cheap and pretty comfortable. To avoid all the negatives, take the luxury classes of buses. You will pay a lot more, but you will have snacks and toilet paper.
Once we arrived in Iquique, a taxi downtown was 1200P/$2 for two. TIP: Always be sure the negotiated price in a non metered taxi is the total and not per person.
After you have wandered around downtown, Plaza Pratt, the Baquedano pedestrian area and the beach/port, you should be thinking about seeing some of the sights outside of Iquique. When we asked a tour operator about a city tour, we were told we had already seen it (so forget it).
We booked a tour for a trip to various archaeological sites. There were other things we could have seen, but lacked the interest. Our trip took about 7 hours and cost 35000P/almost $60 for two. The tour consisted of a van, the two of us and an amiable guide. Seemed expensive, but we got to see things that we would never have had a chance to see on our own. Also, the distances driven were fairly extensive.
The highlights were seeing El Gigante de Atacama and the Pintados geoglyphs. Our driver also took us to see more 'glyphs north of Huara. We had a great day that we will not soon forget (hopefully!).