If you want to explore the city center the most recommended way is to take a walking tour of Split. Other city tours are also available, especially if you would like to explore a bit further than just the historical city center: Bike Tours, Segway Tours, Rickshaw Tours, Bus Tours, Tuk-tuk Tours.
Another interesting city tour is Game of Thrones tour in Split where you visit the most important filming locations in Split and it's vicinity.
Here you can view all city tours in Split.