Is it best to rent a car if flying to Dubrovnik airport w/3nt. stay in the Babin Kuk area, then 4nt. stay in Split, then back to a room near the airport for last nt. as we have a 6:20A.M. flight to catch when leaving? Have heard some say it's better to just rely on public transportation/ferry to Split, & buses from airport to cities. We likely won't be driving much while in Dubrovnik, & in Split only plan to drive to a nat'l. park one day.
Your car will just sit there. It's very easy to take bus between Dubrovnik and Split, but a car would be helpful to get to an out-of-the-way national park. I would rent a car only for that purpose (the other days, you will be paying a daily rate but not using the car, as everything is walkable in both cities). If you can somehow make better use of the car...say to drive to Montenegro or to see Korcula, then it would be worthwhile to have it.
I'm not sure if I understood correctly, are you flying in and out of Dubrovnik? It seems like an open-jaw ticket where you can leave from Split would be better - otherwise you're backtracking. If Split, I know there is an airport bus (I took it) but I'm not sure how early it leaves the center of Split.
But what will you do in those two cities for a week? Just chill and relax? Only one day day trip to the park? You certainly don't need a car to get from Dubrovnik to Split, and you don't need or want a car if you are mostly going to stay in town. For that one day, either rent a car or take an excursion or public transportation to the park.
If as Agnes implies you might be flying home out of Dubrovnik(?) and not Split, you'd want to stay over the final night in Dubrovnik. But you still may not want a car.
If you are flying out of Split, there are public buses and Croatia Airlines buses which are timed to coincide with departing Croatia Airlines flights, though anyone can use the buses, not just Croatia Airlines passengers. If your 6:20a flight is on Croatia Airlines, there should be a bus from the center of Split leaving to get you there on time. I took one of those buses years ago - leaving Split very early in the morning, but it worked out fine to meet my 6:00a flight out. You can dig up a Croatia Airlines Split bus schedule online. There are regular public buses too, but they take longer and not sure where they depart from in Split anymore.
Thanks to both of you for your replies. I'm just getting conflicting info. about cars. Example: Some say we need international license, others say not. Some say driving is super easy, others bring up issues about parking etc. We have to fly in & out of Dubrovnik airport as we'd reserved car pickup there & cost wise it was MUCH less to return it back where we picked it up. So, we can still cancel car, but we CAN'T cancel flights, so must get from Split back to Dubrovnik the night before we leave to be able to catch 6 am flight. We're staying at a small motel that's airport close, but will drive us there early. Just not sure about buses running close to the places we're staying, Babin Kuk area of Dubrovnik at Hotel Neptun, & Apt. Sun Place near Split. I suppose a taxi would be easy to get there from bus drop off? The car rental is very affordable, & we do like the ease it would bring not having to wait for buses etc.
There are plenty of public buses running in Babin Kuk (and all over Dubrovnik) because there are many hotels there. You'll have no issues getting around in either Dubrovnik or Split. Is your lodging in Split outside of the center? If so, then maybe a car could come handy (depends on location of lodging)
I'm still confused...you set up a flight itinerary centered around the use of a rental car? Which you likely won't use on any given day? I would plan an itinerary that at least has some day trips from each city...else the rental car is a waste of resources. A car is great if your trip involves a lot of movement from place to place, or stopping in some areas out of the way.
It doesn't seem like you need an international driver's permit.
https://hr.usembassy.gov/u-s-citizen-services/local-resources-of-u-s-citizens/driving-in-croatia/
Bus info for Dubrovnik:
http://www.dubrovnik-travel.net/bus/
Agnes, thanks much for your help. We can still cancel the car, but not our flights, which were booked w/the idea we'd have the car & car had to be returned to Dubrovnik airport where we picked up at, in order to avoid costly fee. The more info I get indicates we won't really need a car, except maybe the day in Split when we go to Krka park. We stay at Apt. Sun Place in Split, address is Mihanoviceva 50 B, 21000 Split. It's on a hill, & not sure how close to a bus stop it is. Looks like buses run regularly back & forth from city to city. However, the day we leave Split to return to our room across from Dubrovnik Airport, (must catch 6am flight next morn., & motel does offer to take us to airport), could be a problem, as I don't know where that , if one, bus stop is.
I would make sure your place in Split is bus-accessible if you forgo the car. If it's not, then why not pick someplace in the city center instead? You'll be glad you did if the bus schedule doesn't pan out. If you're in the center, you can easily access buses, including a nice little trip to Trogir. Another great thing about Split is the accessibility to ferries to other islands (if you have time for that).
If I were you (unless arriving very late into Dubrovnik), I would go immediately to Split upon landing in Dubrovnik and start your trip in Split, then go back to Dubrovnik and end there. That way, you won't have to split up your nights between towns, and if you can choose lodgings close to the city centers, you wouldn't have to worry about renting a car at all.
Driving is easy in Croatia; parking in Dubrovnik can be a challenge (I never had to deal with that in Split). On my last trip to Dubrovnik, I did have a car and picked a hotel in the Lapad area (pleasant but not particularly charming) and took the local bus to the old town of Dubrovnik, because parking in Lapad was much easier/cheaper to deal with.
Thanks again, Andrew & Agnes. We booked Dubrovnik our 1st 3 nts. as we arrive in the afternoon, & like to be checked in our room before 4pm, & know the drive to Split is 3-4hrs. so wouldn't work for us. Had to be back to Dubrovnik our last nt. due to such an early flight when leaving. I'm going to try & find out from the places we stay about the closest bus stops. As u both said, a car would not really be needed from Dubrovnik airport or in the town, & it looks like we can easily get from there to Split on bus, or maybe catamaran. Once there, looks easy to rent a car for a day trip, or maybe keep it & drive back to airport motel. Thanks again for your help! Appreciate it.