Cafe u dvorištu (meaning - cafe in the courtyard) is one of the calmest places in the city. It's hidden in the passage and you must really pay attention not to miss it. They produce their own coffee and also sell different coffee from all over the world.
Try some coffee to wake you up or just to enjoy the taste, beer offered on tap or in the bottle, tasty teas or home-made juice. They also organize some poetry reading. Enjoy the cozy interior or relax on the terrace, any time of the day.
If you like the coffee, buy some from their roastery right next door.