Mauna Kea Observatory—Hawaii, USA
13,796 feet above sea-level and isolated in the Pacific Ocean, the observatories at Mauna Kea on Hawaii's Big Island offer some of the most pristine star-gazing conditions in the world. Tourists can visit the summit, but officials suggest stopping at the Visitor's Center, located at 9,200 feet, before continuing onward (both to check weather conditions and acclimate to the elevation).
Every night of the year, from 6:00 pm to 10:00 pm. Mauna Kea offers stargazing and star tours to visitors, with telescopes available for amateur astronomers. It's completely free, and you don't need a reservation to participate.
(Part of our special report on Life in the Cosmos)