
There's a small amusement park for children off the main square in town.
And you can go to the mall. There's a movie theater there, but be warned, all the movies are in Spanish.
Get a taxi in the city centre to Chuquicamata. It is an enormous mine open to the sky. There is a free tour to the mine, its worth visiting.
There are frequent bus connections to Antofagasta (2 hours).
If the nearby salt plains appeal, take the 3 or 4 day train ride to Bolivia (bring warm clothes!). The amazing train is essentially a cargo train that carries a handful of Bolivian peasants between the coast and the altiplano, but it provides an incredible vista.
The train to Bolivia runs 2 times a week. Visit FCA's (Ferro Carril Andino) web site for information on schedules and fees.
Calama is not large, but there is not so much to do, so one is likely to take buses or collectivos (shared taxis, that run specific routes) both fairly cheap.