If you are staying in Split and don't plan to continue your trip more south, we highly recommend spending one day to visit the magnificent city of Dubrovnik. The architecture of the city is really something to behold and will leave you breathless. The most iconic characteristic of the city is definitely the massive city wall surrounding the historic center. The city is very rich in culture and history and is the most visited tourist destination in Croatia.
There are some downsides, first being the obvious 3 hour drive which can sometimes be even longer due to traffic and the border you have to cross - the coastal city of Neum is part of Bosna and Hercegovina and you have to pass through this city to get to Dubrovnik. The other downside might be the crowds that you can experience in Dubrovnik. Apart from lots of tourist visiting the city, lots of cruise ships are also stopping in Dubrovnik and you will probably see lots of groups of tourists going around the city.
Nevertheless, there is really nothing that can describe the feeling you get when you are walking on the city walls and hearing the amazing stories of how was this city built and how it has survived it's long and very turbulent history. Apart from the city walls other popular sights to mention in Dubrovnik are the main street Stradun, the Rectors palace, Sponza Palace, Orlandos Column, Lovrijenac Fortress, the Onofrio fountains, Minčeta fortress, Revelin fort, the Maritime museum and the Dominican Monastary. Dubrovnik was also one of the main filming spots for the famous HBO TV show "Game of Thrones" so if you are fan of the series, you will definitely enjoy the scenery which was used to depict the city of King's Landing.