Baku

The UNESCO-listed walled medina is one of the best-preserved medieval Islamic cities in the world — narrow cobblestone alleys, the 12th-century Maiden Tower, the Palace of the Shirvanshahs, and carpet shops unchanged for centuries. Walk it in the morning when light filters through the arched gates.

Zaha Hadid's white undulating cultural center is one of the most photographed buildings in the world — no straight lines, no corners, just continuous flowing curves. The interior exhibition on Azerbaijani history and culture is surprisingly excellent.

Azerbaijan means "land of fire" — and Yanar Dag is a hillside that has burned continuously for centuries on naturally seeping gas. Pair it with the Ateshgah Zoroastrian fire temple 30km from Baku, where flames rise from an ancient altar.

The 15km Caspian waterfront promenade — with the Flame Towers' nightly LED fire display across the water, the Little Venice canal system, and the Baku Eye Ferris wheel — is one of the most scenic urban waterfronts in Central Asia.

65km south of Baku — a UNESCO World Heritage plateau with 6,000 ancient petroglyphs (some 40,000 years old), natural mud volcanoes that bubble and pop silently across a moonscape, and the remarkable quietude of a landscape that has barely changed since the Ice Age.

Azerbaijani cuisine is a Silk Road crossroads — lamb plov (saffron rice), dolma, black tea served in armuda pear-shaped glasses with preserves, and the famous Baku pomegranate sherbet. The Old City tea houses are the place to sit for two hours as the world passes.