I don't completely understand your question. Are you saying you want to come to Croatia only to see Split and Diocletian's Palace and nothing else? Or do you want to plan a Croatian trip that includes Split and other things?
If you want to spend some time in Croatia, what else would you want to see? How much time would you have? When would you visit? Where would you start out - Italy? You don't have to set foot in Italy to visit Croatia - you can fly from the US into/out of Split (or Dubrovnik, or Zagreb) with connecting flights probably in other European cities. Check kayak.com to see the best connections from your favorite US airport.
If you want to start in Italy for some reason, rent a car, and drive down to Croatia it's fairly easy - I've driven most of it. You would drive from Italy through Slovenia to the Croatian border (no border check between Italy and Slovenia.) There's nothing "chancy" at the border with Croatia and Slovenia - it's a routine passport check for American passport holders. Croatia is in the European Union now but not yet in the Schengen Area so there is still a border check.