Dobar dan means “good day” and is the greeting you can never go wrong with.
The story continues through Dubrovnik: it is hot, you step into a cool bar and greet the room as you enter – that is the “day” in the image. There is a tin on the counter for tips. After your cold drink you throw something in, and the landlord thanks you. Tin, bar and thanks give you dobar dan.
Listen to how Ljubica joins the two words together – at normal speed it sounds almost like a single one.