Traveling from Budapest to Croatia

You need to figure out your desired agenda first in Croatia. Dubrovnik and Split - what else?

You can of course train from Budapest to Zagreb directly. You could then fly to Dubrovnik and work your way north to Split. Or train (or fly) to Split and work your way south. (Many people would recommend a stop at the amazing Plitvice Lakes National Park about two hours south of Zagreb, FYI. I would.)

I assume there are no direct flights from Budapest to Split or Dubrovnik or you would have already found them.

In the summer, you probably have more seasonable flights between Split, Dubrovnik and various cities in Italy. I know there are direct flights now a few times a week between Dubrovnik and Venice as well as Split and Venice. Perhaps Milan and Rome too. Just do some checking - use Google Flights and Skyscanner.

There are no direct flights from Budapest - a train seems to be the best way to travel into Croatia. I didn't think about flying to Dubrovnik, that looks like a great alternative, thanks! And there are also plenty of flights from both Dubrovnik and Split to Rome, so that works out as well. Trying to plan my itinerary in Croatia now so I'll be sure to include Plitvice Lakes, thank you!

There are direct flights to Podgorica and from there it's only a few hours along the beautiful Bay of Kotor to Dubrovnik; although I would stop in Kotor and spend at least one night in Perast.

There are direct flights to Podgorica and from there it's only a few hours along the beautiful Bay of Kotor to Dubrovnik; although I would stop in Kotor and spend at least one night in Perast.

Would you recommend renting a car or taking a train?

No train service. I would (did) hire a guide. I went in the other direction. I loved Montenegro and returned the next year. I have also flown to Dubrovnik from Budapest through Belgrade. Had to spend a night in Belgrade, but loved the city and will be back there as well.

There's also bus service from Podgorica to Kotor and from Kotor to Dubrovnik. I don't know how the schedules fit together, though. Note that there are a lot of places in Montenegro that are more appealing (at least superficially) than Podgorica; it is, however, a useful transportation hub.

You will almost certainly find that there is a painfully high drop charge if you want to rent a car in one country and drop it off in another.

Podgorica isn't a place i would want to spend a lot of time. I've overnighted there a couple of times and it has one sort of interesting district but otherwise its just a good transportation hub. Outside of Podgorica, Montenegro is a beautiful country with some great old towns, mountains, lakes, monasteries, etc....