Wow. This is only the second time we’ve stumped you with Where on Earth; the first time was coincidentally within the same country of Georgia.
Those who guessed Turkey came closest. The former Soviet Republic borders Turkey and naturally shares some of the same limestone geology that makes a cave city such as the one featured above possible.
This particular location, Vardzia, was built (or, rather, dug) in the 12th century and at its peak, was home to 50,000 troglodytes living amongst 13 floors of caves and tunnels. Although a major earthquake in the 13th century destroyed much of the cave city, there is still a substantial amount left to provide an entertaining day of tunneling and exploring. Be sure to bring a flashlight, however. Some of the tunnels are long and dark and can be quite intimidating without a guide.