Palermo to Dubrovnik itinerary, using ferries and train

Rail passes don't cover any ferries between Italy and Croatia. And of course, Dubrovnik is not served by trains, which only go as far south as Split in Croatia (and are cheap there). Unless you have a specific route in mind, I recommend flying.

When you Google "Palermo to Dubrovnik flights", you'll see no direct flights, but a connecting flight via Lufthansa (4 hours 20 min+). Dubrovnik in general is not the easiest to get to, unless you're either coming from Split (easy bus ride) or a ferry from Italy (there may be direct flights from Italian cities like Milan, but not from Sicily - Google it to check). Ferries and train won't work in this case.

You can fly for about $100 from Palermo to Dubrovnik.