Croatia from Italy

Four nights is only going to give you three days in Croatia, plus a few hours. I'd start by investigating your flight options back home. I was able to get to Washington DC from Zagreb with only one stop. I don't know what you'll run into from Dubrovnik or Split; that will depend partly on your home airport. The flight situation may affect how you structure your time in Croatia.

With your tight timeframe, your only real choice for traveling from Rome to Croatia is to fly. See what you can find on skyscanner.com for your travel date. It appears there are non-stop flights from Rome to both Dubrovnik and Split.

Mid-July is peak season in Croatia; from all reports Dubrovnik will be a zoo, but you could stay there and try to be out of the city center during most of the day-tripping hours.

I think Plitvice Lakes National Park is too ambitious for a short trip like this focused on the coast. Perhaps either Split or Dubrovnik plus an island could be managed. Definitely do not try to see Plitvice on a day-trip from Split. That does not make for a good experience because of the extreme crowding on the walkways.

Great points to think about! Thanks for the info!

I would avoid Dubrovnik. Croatia has many towns like Dubrovnik, but which don't get the tourist insanity and July is the height of tourist insanity. I would go to Split, and stay there. Split is the site of the retirement villa of Diocletian, the important Roman emperor at the end of the 2nd century. There's the palace itself, which is worth a day. It's part mall, part archeological monument. Do the tour of the plumbing on the lower level. There is a fine Archeology Museum in Split. You can do a day trip to Trogir for the "Croatian limestone coast" experience. There's a fine sandy beach for a beach moment. There are many nice restaurants. If you wish, you can do the day trip to Plitvice Lakes, or to Krka National Park. You can easily find an inexpensive sobe (Croatian AirBnB) on booking.com. There are a ton in Split.

While it will be easy to get to Croatia by flying, you may encounter more costs/hassle flying home.
I would not do it for only four nights, but in order to visit Plitvice--assuming you meant that park, it would probably be best to fly to Split and then fly home from Zagreb. Pretty rushed.
If you want an alternative in Italy that would be somewhat similar in a nature-excursion kind of way, you could take a train to Ancona and then go to Sirolo on Monte Conero--the coastline there reminded me a lot of Croatia. I would only do that if you can fly home from Ancona. The coast south of Salerno near Sapri also has striking similarities to the Croatian coast. IF you could bear to pass by the Amalfi coast and get down there.
Not too far south of Rome, Ucellina park is wonderful (but in July maybe too hot and buggy).

Thanks so much for all the feedback! Everyone has given me a lot to think about.

Italy and Croatia is one of those country pairs (like Spain and Portugal, or Greece and Turkey) that seem "natural" and "easy" to those of us in the US, but are actually far more difficult than one would think. While you certainly can fly from Rome to Croatia, flights back from Croatia to the US can be surprisingly complicated and expensive, as Acraven correctly pointed out. Starting this summer, for few months of the year American Airlines will have a nonstop flight from Dubrovnik to Philadelphia; otherwise, there are no nonstop flights from anywhere in Croatia to anywhere in the US at any time, and you may have to make multiple connections to get home.

So, do investigate these things before committing to an itinerary. And unless you have your heart set on just seeing 1-2 places in Croatia (and spending a good amount of time in transit instead of seeing places), with only four days you'll do much better to just see more of Italy, and see Croatia on a separate trip.