The Atacama Desert in Chile is the driest place on earth, which contributes to making it an exceptional place for stargazing and why the European Southern Observatory operates 2 major observatories in the area.
There are several organised stargazing tours, which are excellent as nobody wants to carry a large telescope on their travels. The tours run most days except for around a full moon. However, if you are lucky enough to be in the area for a "blood moon" lunar eclipse then the tours will be running and they are well worth it! There is nothing like going out after dark (or in my case at 3am) in the freezing cold to stare at the sky for several hours.
I went out during a blood moon with Atacama Desert Stargazing for a magnificent time. I've never seen the sky lit up in all its glory like that before. Also, I was able to connect my camera to one of the telescopes to get some amazing close ups of the moon during its eclipse.