Padua to Plitvice

Have you determined where you are flying home from? I know you did not intend to include Istria, but you could take a ferry from Venice and rent a car in Rovinj or Pula, or check flights to Zagreb, Split, and Dubrovnik. I am not seeing any direct flights from Venice, but I do see some from Milan.
With ten days and that list, I’d shoot for into ZAG and out of DBV or vice versa, with roughly equal nights everywhere except Plitvice, which only needs a night. I’d actually put more nights on the island but you should assign the nights according to your interests.
You can omit the car other than to and from Plitvice. You can always do a rental for a day on an island if needed, yet that will save you from having to limit yourself to car ferries as there are many more passenger only catamarans. July and uncrowded is a tall order, but take a look at Lastovo.

It will probably maximize your time to start at Plitvice and end at Dubrovnik, as otherwise you’d need to get to the closest airport from Zagreb and then you may need a night in Zagreb. If you fly into Zagreb for example, you could potentially be in Plitvice by the afternoon, enjoy a walk them and stay the night and explore more the next morning, then head to Split for x days (drop car), boat to island for x days, boat to Dubrovnik for x days and fly home from there.
Airport to check as there could be seasonal flights not showing up now: ZAG, SPU, DBV, with ZAD a lesser possibility. In Italy, check Venice, Bologna, Milan

I think the best option is probably a quick flight from Marco Polo (very easy to reach by bus) to either Split or Zagreb.

Split is probably ideal, because you’re closer to both Plitvice and access to some islands (Hvar, Brac, Vis) and some coast towns like Sibenik, Zadar or Trogir.

Zagreb is still convenient and gets a lot more flight connections. Renting a car there and heading down to Plitvice is pretty straightforward. You’re just a couple more hours from the coast at that point.

At that time of year, you will 100% need a night in Plitvice so you can visit the park both late and early. It will be thoroughly mobbed through the meat of the day. I’ll note too that both Zagreb and Split are worthwhile destinations in themselves and worth a couple nights easy. I’m particularly fond of Zagreb and think it’s very underrated.

I would stay far, far away from Dubrovnik this time around. You could also make your way to Istria via ferry, bus or car and start there. But for my money, I think a flight gets you straight to the matter and would be worth it. Check with Croatia Airlines directly, you might find something that fits.

Plitvice Lakes National Park is quite a bit closer to Zagreb than to Split, in terms of both distance and driving time.

I quite like Zagreb and don't find Split all that interesting, but if your focus is on the coast and the islands, you might prefer to start in Split. It will just cost you an extra half hour of driving time or a bit more.

A great ten days in Croatia would start in either Split or Dubrovnik, and take one of the catamaran boats ( Krilo or TP Line) to Hvar and Korcula. The catamarans dock directly at Korcula Town and Hvar Town, which the larger ferries are unable to do, Plitvice Lakes National Park is a place you’ll want to overnight at in order to enjoy the park in the afternoon after checking into your accommodation and again the next morning before departing. That way, you will avoid the mobs of people who throng the park during July— mostly between 10:30am and 3pm.

After Padua, I would suggest flying from Venice airport to Split to begin your trip. Rental cars can be problematic while visiting Split and Dubrovnik due to parking and traffic congestion. You might want a rental car, however, to travel from.Split to Plitvice as buses take five hours.

www.DirectFerries.com. has info on catamaran schedules and fares.