The Four Seasons brand is synonymous with luxury. And the Four Seasons Hotel in Baku is elegance with old-world charm. I first discovered this incredible property on the trusty old Instagram. I knew if I ever visited Baku, the Four Seasons was where I was staying. Located centrally between the modern city and along the medieval walls of the old town. Only minutes away from the trio of flame-shaped modern towers and steps from the Caspian Sea.  The Arrival Baku was pleasantly surprising. Arriving into the modern Heydar Aliyev International Airport was not what I was expecting of a country straddling Eastern Europe and Western Asia. The new terminal was opened…