When I visited Split, I immediately had mixed feelings about the town. Even though it is listed as a UNESCO world heritage site, I did not find the harmony I expected, among the modern area which did not really charm me and its historic centre overrun by tourism. Diocletian's Palace is definitely still a fabulous ancient monument, that is still worth visiting, and its seafront view lined with palm trees provides a lovely setting for a stroll or a drink, but it's not a town that I would advise people to stay in for very long, as I prefer the charm and peacefulness of the Croatian islands or smaller towns.
Split also has many museums including the museum of Fine Arts and of archaeology which for me offer two complementary ways of discovering the history and culture of the region. But if you had to visit only one place, it would be the house of the Croatian sculptor Ivan Mestrovic, which faces the sea and has wonderful architecture and surroundings.
Finally, an evening walk on the Marjan hill for a beautiful view over the port during sunset should leave you spellbound.