Prague - 4 nights >>> Fly to Budapest (only Ryan Air flies between the
two cities)
Normally I would say 4 nights is more than I would want, but it is your arrival city after a very long flight (I flew Sydney to Budapest a few months ago, I understand). So maybe the 4 nights makes sense. Your idea to fly to Budapest makes good sense and is exactly what I would do.
Budapest - 3 nights (but I have heard 3 nights is insufficient) >>>
Train to Vienna.
Yes, when you figure the first day is a half day at best, 3 nights does come up short. While its not what I would do, if its all the time you have then better to see it fast than not at all. But 4 nights would be much, much better and 5 would be ideal. If you click on my name it takes you to my information page where I have a few links on Budapest that might be useful. Watch this video and the one below about Vienna. Same guy, both pretty well done: https://youtu.be/1nd5AtZIrTk?si=EEZ6Kqo4D3VNHfvM
Vienna - 4 nights >>> Train to Salzburg
This comes down to what sort of things in life you enjoy. Those that love Budapest enjoy Vienna a lot less, and the reverse is true. So research the heck out of the two and make sure its Vienna that will most captivate you. If you have any doubts, then move one day to Budapest. Just my taste, my interests, but 3 nights in Vienna would be fine. But I would take a fairly early train out of Budapest to get the most out of the time in Vienna. Video: https://youtu.be/HhuP2_Cf-54?si=lBFbzlqjHxH-699Y
Salzburg - 2 nights (might have almost 2 full days if we catch an early train from Vienna)
I haven’t been to Salzburg yet. I go in September. From my research and knowing what I enjoy, I would spend the morning in Vienna and take a train after lunch, even midafternoon. Then the 2 nights would work well for me. Video: https://youtu.be/X6bGQ1OMk0U?si=Zz9BVrqD1-M7kCkl
Private Transfer from Salzburg to Munich Airport.
If you flight is late afternoon, then think about Daytrip.com and make a stop or two along the way so the day isnt all about transportation.
Okay now I see your update
So would you then suggest 4 nights per city is sufficient? 4 - Prague
4 - Budapest 4 - Vienna I could possibly do some day trip from Vienna
to see a smaller town?
So fly into Prague and do 4 nights
Then fly to Budapest for 4 nights
Then Vienna for for 4 nights and fly home from Vienna?
That’s better, but I would still only do 3 in Vienna and only 4 in Prague because it’s the arrival city.
For something smaller and interesting, you could stop in Gyor on the way to Vienna. I like it better than Bratislava and Bratislava is a detour while Gyor is on the train track from Budapest to Vienna. Another close easy small town out of Budapest is Szentendre.
And I think skipping Salzburg is wise until you have first seen and spent enough time with the big three.