The Meson de la Flota is the quintessential tavern. Relatively dark inside and with a great flamenco band, which is basically headquartered here, this makes for a good intimate atmosphere. You do need to bear in mind that the flamenco group, while extremely good, is also very loud so forget about a romantic chat if they are playing.
The service is typically very good and they serve some of the best sangria in Havana. Food wise, I think that the tapas are pretty spot on (spicy potatoes, chorizo and shrimps in garlic being the highlights). In fact, so much so that I would recommend loading up on tapas and missing the main dishes, which are not as good and are less value for your buck. This place has a tablao flamenco (wooden stage), where dancers and musicians, such as the Havana Flamenco Company and Ecos, perform daily.