Although Split is open museum, with Diocletian’s palace as one free museum you can walk through, there are many specified museums you can visit if you want broader cultural experience. Practically all the museums are within walking distance. 50% of all sold museum tickets goes to Gallery Meštrović which contains numerous sculptures of the most prolific Croatian sculptor Ivan Meštrović. However, the life of Meštrović is almost as amazing as his work.
If you are fan of art, the Gallery of Art in Split is place for you. It was hospital, and Museum of Revolution during Yugoslavia.