Scrapping Ireland vacation plans, going east.

I see lots of info on other posts......but what about drive or train?

I don't see any advantage to driving as all three cities are best seen on foot, and you can easily get between them by train.

Renting a car in one country and dropping off in another almost always results in a large (often stunningly large) "drop-off fee". I'd take the train.

There is tons to see and do in three of those cities; Bratislava is smaller, but I assume you'll still have a full day's worth of stuff to do there. So those four places are really going to completely fill your trip. In fact, as you dig into guide books, I think you're going to find that you cannot see all that you want to. You mention about three days in each city (I think Bratislava needs less), but to have three days in a city, you need to spend four nights there. Two weeks sounds like you will not be able to spend four nights each in Budapest, Vienna and Prague plus even two nights in Bratislava. Exactly how many nights can you spend in Europe, not counting the night on the plane? I ask, because often the answer is "twelve", and that's not much time for three major capital cities plus a smaller one.

Given your target list and the length of your trip, I don't see how you can possibly have time for wandering around the countryside, which is what a car is useful for. As you know, a car is useless in a major European city, plus expensive to park.

Definitely take trains. And I'd suggest doing some sightseeing research to see whether you'd be better off with just three destinations rather than four.

I think your timing is good. Weather is unpredictable, and you should be prepared for occasional rain (I was hailed on in Budapest last May), but that part of Europe can get unpleasantly hot later in the year. I chose to begin my trip on May 2, and I was glad about that decision.

If you plan to land in Europe on May 1, do check on closures. I don't know that they are significant in the countries you propose to visit, but May 1 is Labor Day in France, and there was no public transportation available from the Nice airport into the city on that day in 2017.

This is a train itinerary, no question about it. Drop fees for one way rental might be hundreds of dollars. As Rick says, a car is a worthless headache in big cities. And it’s so easy on the train.

Lets see,

Budapest to Bratislava - 3.5 to 4 hours hotel door to hotel door
Bratislava to Vienna - 2 to 2.5 hours door to door
Vienna to Prague - 5.5 to 6 hours door to door
Total travel time 11 to 12.5 hours

Never been to Bratislava, despite being within 1.5 hours of it 2 or 3 times a year. Too much else that sounded more interesting (like every place else in Slovakia or Eger, or Cesky Krumlov)

Everyone enjoys something different. For my taste
4 full days in Budapest
2 full days in Vienna
3 full days in Prague

Another day free? Add it to Budapest
Still another day free? Go to Eger or Cesky Krumlov; or i guess even Bratislava.

Oh, and Labour Day, aka Labor Day, May Day, International Workers' Day and A munka ünnepe is a great time to be in Budapest. Lots going on. See you there. https://expat-press.com/may-day-2018-hungary/