Italy and Croatia Trip Planning Help

This type of trip just takes legwork. If the order you listed them is your preferred order, then I would start by checking open-jaw flights into Milan, Genoa, Pisa, and Florence (for access to Monterosso) and out of Zagreb or Split (for Plitvice or Krka national parks, which are the parks I am assuming you mean). For different orders, include Naples and Dubrovnik in the mix. It is just a lot of time on kayak!
I would think there would be some seasonal flights to Croatia out of Naples, but you may have to get to Rome after that bit. Try sky scanner for searching flights. The ferry from Bari is probably too time-consuming. good luck!

We traveled from Italy to Dubrovnik in October 2016. At that time there was only one viable ferry operating. We traveled overnight from Bari to Dubrovnik. If we had traveled earlier, there were ferries from other west coast cities.

Our trip started in Naples. We rented a car and drove to Pompeii and the Amalfi coast. We then visited the heel of Italy before leaving for Dubrovnik.

I had checked out flights, but getting to Dubrovnik was challenging. So look for ferries from various west coast cities and get to that city in the best way possible.

Dubrovnik is a beautiful city, but it is only worth a couple of days in my opinion. You may wish to consider a small boat tour of the coast and some of the island.

Enjoy your trip.

I am also planning an Italy/Croatia trip for September 2017 (flying into Rome, home from Venice, but most of my time will be in Croatia) and have also discovered that travel times between cities and countries can be great. Rome2Rio dot com has given me some direction. I use that website to find out what airlines might fly between two cities, and then go directly to that airline's website to look for actual dates and times. For example: Vueling has direct late morning flights (40 euros!!) between Rome and Dubrovnik. Croatia Airlines has direct flights between Split and Venice. They also fly frequently into Pula from Split and Rome. I've also found that little Mistral Air (which mostly flies pilgrims to and from Rome and pilgrimage places) has a direct flight on Fridays (during the season) between Mostar and Rome. And Volotea Airlines has flights between Dubrovnik and Venice and between Split and Venice. Many of these connections, above, are only 2 or 3 days/week. Lots of these will not show up on my usual sites like travelocity or expedia. And some are only seasonal. Keep looking! Good luck!

I went from Sorrento to Dubrovnik in 2008 using a combination of train and ferry. Since you’re in no rush to get from point-to-point, that could be a good option for you. Travel would include a local train from Napoli Centrale to Caserta, changing to a Freccia or IC to Bari Centrale. You then take a city bus (don’t remember the number) from the train station to the port to pick up your ferry tickets. The bus stop is in front of the station and the driver will let you know when you’re at the port bus stop. I joined some people I met while waiting to board for a farewell-to-Italy drink at the bar on the tail of the ferry and we watched the lights of Bari fade into the distance – very chill. I’d suggest getting a cabin with shower, which is only slightly more expensive. While the shower is simple, a hand-held mounted to the wall, it was really nice to freshen-up after the previous day’s travel and especially if you won’t be able to use your Dubrovnik room until midday. If you choose this option and presuming the voucher process hasn’t changed, be aware of the deadline to pick up your ferry tickets at the port and don’t cut your trains too close. There’s a café at the port where you can relax, get a snack or drink and chat with other travelers while waiting to board.

Edit: I misread your post (you're looking for shortest travel time), but I'm not going to change my original post in case you reconsider or the information is useful to someone else.

Glancing at Skyscanner, it looks like Easy Jet flies direct from Naples to Dubrovnik on Mondays, Wednesdays, and Saturdays in July. From Rome, you would find more flights.