Recommendation for Dubrovnik-Split-Zagreb?

Hi! I’m planning to visit Croatia for a week and I'm looking for recommendations for Dubrovnik , Split, and Zagreb, things to do, places to visit, food to eat, avoid tourist traps if any. I'm interested in exploring the history, culture, and everything the country has to offer.

I do plan to visit the city walls & Iron throne in Dubrovnik, Island hopping in Split. I'm not entirely sure about Zagreb. As Zagreb is quite big what area would you recommend?

Thank you!