Buza (Croatian for "hole in the wall") is Dubrovnik's most celebrated cliff bar, reached through a literal hole in the city walls on the southern side of the old town. You follow signs that say "cold drinks" through a narrow passage and emerge onto a series of rocky terraces perched above the Adriatic, with a direct drop to the sea below. The views of the open sea and the Dalmatian coast are spectacular, particularly at sunset.
The setting is the entire point — the drinks are standard and overpriced, the seating is basic rocks and plastic chairs — but nobody comes to Buza for the cocktail list. Go in the late afternoon, find a ledge on the lower terraces, and wait for the sunset. People jump into the sea from the rocks below. It gets crowded in high summer; arrive early to get a good spot. There are actually two Buza bars nearby; the lower one (Buza II) is slightly less crowded.