Would it be somewhere in a desert a long way from water and mist, or high on a mountain above the lower atmosphere? Where is the best location in theory or in practice?
- High altitude, so there is less atmosphere to look through.
- Dry climate, so there is less water vapour, fewer clouds, less rain.
- Low latitude, so more of the sky is visible for at least part of the year.
- Remote from non-natural light sources.
And there are lots of non-science considerations: political stability, good transport links, good network connectivity, skilled local labour, no indigenous land rights issues. All these factors have to be balanced against each other.
There isn't a single "best" place, but Mauna Kea in Hawaii, La Palma in the Canary Islands and Paranal in the Atacama desert in Chile tick a lot of the above boxes.
The best sites for telescopes are where they currently are and where the even bigger next generation of telescopes are being built. These sites are Mauna Kea in Hawaii, Roque de los Muchachos on La Palma in the Canary Islands, the Chilean Andes (sites near La Serena—Cerro Tololo, Las Campanas—and in the Atacama desert south of Antofagasta—Cerro Paranal), and in the Arizona mountains near Tucson—Kitt Peak and Flagstaff—Lowell Observatory.
For optical astronomy, the main factors that determine the "quality" of the site are the "seeing" (this is the extent to which the atmosphere around and above the observing site blurs the images of stars), the fraction of clear observing nights and the darkness of the night sky when the Moon is below the horizon. All of the sites listed above do pretty well on all these scores.
It's unlikely that there are significantly better sites elsewhere in the world. There has been extensive site testing at various other promising locations, but the ones I've listed generally come out on top.
Of course if you move to longer (infrared) wavelengths then the answer would be different. High altitude is then really important, to reduce the mass of water vapour overhead, and also the atmosphere and telescope are significant thermal sources of background—and so in theory putting a large infrared telescope on a mountain near the South Pole would be a good idea, but very difficult in practice.