Few cities tell their story in one frame like Baku: glass Flame Towers glowing behind the walled UNESCO old city. Icherisheher's Maiden Tower and Shirvanshah palace, the 1909 Caspian boulevard, Zaha Hadid's Heydar Aliyev Center, and the strange half-day: burning Yanar Dag, mud volcanoes, Gobustan petroglyphs. Stay near Fountain Square; Azeri grills suit Gulf palates and halal is easy; add two green days in Gabala/Sheki.