Azerbaijan bills itself as the Land of Fire, and it earns the title. On a hillside about 25 km from Baku, Yanar Dag has burned continuously for decades, fed by natural gas seeping through porous rock — no wood, no visible fuel, just a wall of flame across the slope. It's most striking at dusk, and 20 to 30 minutes on site is plenty.

The capital is the obvious base. Baku stacks glass towers, Soviet blocks and a walled medieval Old City along the Caspian shore, and the contrast is the appeal. Priorities: the Flame Towers lit up at night, the long waterfront promenade of Baku Boulevard, the curvilinear Heydar Aliyev Center designed by Zaha Hadid Architects, and Icherisheher — the UNESCO-listed Old City, home to the 12th-century Maiden Tower and the Palace of the Shirvanshahs. Sleeping inside the walls means you get the cobbled lanes before the day-trippers arrive.

Two day trips round out the Baku stay. An hour south, the Gobustan plateau holds more than 6,000 petroglyphs spanning roughly 40,000 years — hunting scenes, dancers, boats — plus bubbling mud volcanoes nearby, best reached with a driver or tour because the final roads are rough. Yanar Dag and the Absheron Peninsula fill another easy day.

For a slower stretch, head five to six hours inland to Sheki at the foot of the Greater Caucasus. The UNESCO-listed Palace of Sheki Khans, an 18th-century summer residence, has painted interiors and shabaka windows assembled from wood and coloured glass with no nails or glue. There are merchant caravanserais to wander, and Sheki halva — layered nuts, syrup and pastry lattice — is the local must-eat. Overnighting here beats a rushed day trip.

Give the trip at least a week; nine or ten days lets you linger. Spring and autumn are the comfortable seasons for pairing the coast with the hills, and it's worth checking the dates of Baku's annual Formula 1 street race, which sends hotel prices climbing even if you're not going. Many nationalities can arrange entry through the official ASAN e-Visa portal, typically issued within three working days.