Since there is often slow-moving line for the cable car to Mt Srd, I’d go there first, immediately after disembarking. When we visited a few years ago, there was a small museum and art exhibition up there, but unless they’ve added some signage, you will have to ask. I recall it being hidden if your focus is the view. It’s called Dubrovnik During the Homeland War, as I recall. The Stradun is wide enough to breathe, but always crowded. Take one or more of the staircases up to get a different and cooler view. In addition to the Cathedral, I remember a couple other churches; the Orthodox Church of the Assumption had some beautiful art. The fountain won’t take any time at all. The palace wasn’t that big of a deal for us either. I remember it being mostly modern art, but maybe that has changed. Near that, though, there was a moving little museum/exhibit/memorial dedicated to young men who died defending the city. I distinctly remember the haunting photos of the faces of those men and the pictures of the destroyed Stradun. Comparing them to the present day gives an excellent idea of the scale of Dubrovnik’s rebuilding. I don’t see it mentioned much, but a few blocks off the Stradun, there was a fascinating and very well-done ethnographic museum that gave a good overview of clothing, arts and crafts, agriculture and family life in the countryside. You might consider the Maritime Museum, which talked a lot about Dubrovnik’s role as a maritime power during the rule of Venice. Interesting enough, but more of a niche museum. My husband, who was a sailor, loved it, but I found it a bit dull. However, like the ethnographic museum, I would expect it to be less crowded. I don’t know what time it closes, but I would save the wall for last. People are likely to head there first and it’s hot up there. Whenever you go, take a hat and water. Being there until midnight will be plenty of time, but check the hours of everything before you decide what to do. I can’t remember how late things were open.
