Baku's sights split between two distinct cities. The first is the walled medieval Old City, Icherisheher, where the Maiden's Tower, the Palace of the Shirvanshahs, and a tangle of caravanserais and mosques fit inside an area you can walk across in fifteen minutes. The second is the oil-boom and post-Soviet city around it — Belle Époque mansions along Istiqlaliyyat Street, the Stalin-era seafront boulevard, and contemporary statements like the Flame Towers and the Zaha Hadid-designed Heydar Aliyev Center.
Allow at least three full days. The Absheron Peninsula day trips to Yanar Dag and the Ateshgah Fire Temple tie the city to its ancient association with petroleum and fire worship, and shouldn't be missed.