Copiapó's real value is as a base for the surrounding desert and mountains. The city itself can be seen in a day; the landscape around it is extraordinary and justifies staying longer.
Bahía Inglesa and Caldera (70 km west) is the nearest escape — turquoise water, white sand, and good seafood. The port town of Caldera has colonial architecture and a fish market. Easy on any road in a standard car. Allow half a day or combine both into a full day.
Mina San José Memorial (45 km north) requires a vehicle but is a straightforward drive on paved road. The memorial to the 2010 mining rescue is sober and worthwhile; the landscape around the abandoned mine is bleakly evocative.
Parque Nacional Nevado Tres Cruces (145 km east) needs a full day and a 4WD. The salt lakes — Laguna Santa Rosa, Laguna del Negro Francisco, Laguna Verde — and the flamingo colonies are remarkable. Acclimatise before pushing to altitude; the park starts at 3,700 metres.
Ojos del Salado is the world's highest active volcano at 6,893 metres, accessible as a day drive to base camp (4,200 metres) even without climbing intentions. The views of the peak from the approach road are stunning. Climbers who intend to summit typically spend several days acclimatising in Copiapó and at intermediate camps.
Salar de Pedernales is a large salt flat southeast of Copiapó, off the beaten track and less visited than the main parks. Pink flamingos congregate on the salt lake, particularly in summer. You need a 4WD and ideally a guide — the roads are rough and poorly marked.