This is mostly because the experience is not really about drinking coffee, but more about socializing. However, there's no doubt that the relatively high price of coffee in Croatia has something to do with it too.
So, all visitors to Croatia (and especially Dubrovnik) must take the time to sit and "take a coffee" at least once during their stay.
Coffee drinks served at most cafes are similar to those served in Italy or in Austria; after all, Croatia inherited its coffee drinking culture from these nations.
Popular drinks include the cappuccino, bijela kava (white coffee, like a café latte), and espresso. For Americans looking for American-style filter coffee, you won't find it here; the closest thing is an americano, which is a shot of espresso diluted with hot water.
Also popular with locals is Nescafe, an instant coffee drink made from a powder; it's fairly sweet and not as strong as a real espresso drink. One other drink worth mentioning is the iced coffee; in most cases this is not just coffee on ice, but a drink with espresso and ice cream.
Now that you know what to order, the only question left is where to enjoy your coffee. Croatia, and Dubrovnik in particular, has no shortage of cafes.
The cafes lining the Stradun in Dubrovnik's Old Town certainly look inviting, but there are a few things to consider first. A coffee on the Stradun can cost as much as twice that of one just a couple of streets away.
In addition, during the summer months most of the other patrons will be tourists. Of course, I'm not suggesting that you shun the Stradun all together; a coffee in the sun on Dubrovnik's most famous street can be an unforgettable experience.
For a genuine feel, I suggest taking a seat at Café Festival, the only café on the Pile end of the Stradun. Or for a truly old-world Viennese style coffee house, check out GradsKavana, just off of the Stradun near St. Blaise church and Rector's Palace.
Outside of the Old Town the price for coffee drops dramatically, but the choices do not. There are several nice cafes on the pedestrian-only Setaliste Kralja Zvonimira in Lapad, and Iva Vojnovica is home to several modern, trendy café bars popular with young locals.
You'll know it by the line of Mercedes parked on the street and the Gucci and Prada sunglasses peering out from inside the cafes. Another great, but expensive, option is to have a coffee in one of the many beautiful hotels in Dubrovnik.
I particularly recommend the Dubrovnik Palace in Lapad for the great coffee, good service, and spectacular views. The service and coffee are also tops at the Hilton Imperial Hotel and the Hotel Bellevue.
If you enjoy drinking coffee, I would suggest trying a few different cafes until you find one that suits you. It may turn out to be a small café frequented only by locals or one of the busy cafes on Stradun with tourists vying for the best tables.
Either way, you will have experienced an important part of Croatian culture by taking the time "to take a coffee."