Was born in Baku and my opinion is certainly biased. All foreigners that I know who visited Baku admired it (or at least they didn’t tell anything esle in my face :) The best part is the old “inner” city (Ichari Sheher, part of the UNESCO world heritage, http://whc.unesco.org/en/list/958) and also the “European” part of the city built mostly during first oil boom. You will apreciate the food, music, architecture and everything that has history in its name. Ask locals to show you around, as the city has many hidden treasures.