Old Town
From Split, it is a funny drive down to Dubrovnik. Funny because you actually leave Croatia for a brief moment and enter Bosnia so that you can get to the other side.
If you are a person that is into castles and ruins and the likes, you will love Dubrovnik. And if you love Game of Thrones too. This is essentially the King's Landing in the Game of Thrones. The city centre is built within these tall castle walls as Dubrovnik used to be a location that was often attacked by other armies.
Activities that we did in Dubrovnik include sea kayaking and chilling at the beach. A walk in the entire old town square can also easily take a whole day since the tour of the castle walls (think it costs $20) takes 2-3 hours. There are also nude beaches that you can go to but my friend in charge of the Dubrovnik itinerary was too shy to go there =(