On your second day, visit Heydar Aliyev Center, designed by renowned architect Zaha Hadid. The architecture alone is worth the visit, and it has affordable entry fees. Afterward, head to Fountain Square and the nearby Nizami Street, which is full of affordable cafes, shops, and galleries where you can experience the local atmosphere. In the afternoon, explore the Baku National Museum of History for a small entry fee, where you can learn about Azerbaijan's ancient and modern history. End the day by relaxing in Upland Park, which offers fantastic views of the city and the Caspian Sea. The park is free to access and a perfect spot for watching the sunset.