If you have a fat wallet, speak some Castellano [Spanish] and like a challenge then rent a vehicle. For serious exploration it should have high ground clearance, though 4WD is not vital.
Air conditioning is close to essential unless you don't mind arriving at your destination with a melted face and dressed like you've just climbed fully clothed out of a swimming pool. Atacama is a very hot destination.
Many of the rentals are 4 seater pick-up trucks, presumably since that's what locals want when the car gets sold on a couple of year down the line, though it's not ideal as you clearly can't lock your baggage away nor can you protect your peanut butter from melting in the blazing sun. On the positive side people who get car sick from the inevitable bouncing over very rough tracks are magically cured by rides in the back, clutching the roll cage and road surfing.
The easiest place to rent wheels is on arrival at Calama airport, needing just an hour's drive to get to San Pedro.
