A small chain of coffee shops with several branches across central Baku, Coffee Moffie does a serious flat white and the city's best baked goods — proper croissants, sourdough toasts, and a rotating set of cakes. The Nizami Street branch has decent wifi and is a good place to write postcards or wait out the afternoon heat.
It's not a cultural experience and the design is anonymously Scandinavian, but if you've been on the road in the Caucasus for a few weeks and want a properly made coffee, Moffie is reliable.