In Cuba you do not usually drink much tea, I imagine it is because of the hot climate, the fact is that I have never seen or visited any tea house, although it is usually sold in some establishments, but it is not common, the common thing here is coffee, and cafes if there are many. There are also places where coffee is the protagonist and they specialize in serving a varied menu based on coffee.
Cubans are very fond of black nectar, as it is also called. So my preference would be a coffee shops.