Help needed in planning a tour of Austria, Budapest & Prague

I suggest that you buy a few good guidebooks and do some of your own research first. There is also plenty of information online. Here is a place to get you started with Austria - https://b2b.austria.info/uk/

Perhaps once you have explored the area further on your own, you can come back here with your proposed plans and we can provide our thoughts.

May to September is the best time regarding the weather.

If you are an aficionado of opera and/or classical music, note that in Vienna the high class offerings are scarce during the summer break (July and August).

To avoid unnecessary traveling the best order would be Prague-Vienna-Budapest (or the other way around). Try to get according open jaw flights. Air fare to Prague and Budapest is usually lower than to Vienna.

I would suggest for Budapest and Prague 3 days each, the rest for Vienna (with possible day trips to Salzburg and Bratislava).

thanks for your valuable inputs

Many people recommend spending a night in Cesky Krumlov between Vienna and Prague.

2 nights = 1 full day to sightsee, since you'll use 1/2 day or more each time you move. I'd say a minimum of 3 nights in Prague (1 more for a day trip to Terezin), 3 nights Vienna (1 more for day trip to Melk) and 3 nights Budapest. I would probably add a night to Budapest before I added to either of the others, though it's easy enough to fill another 2 days in each of those cities.

Given a choice, I would plan to travel 3rd-4th week in May or end of May-beginning of June.

Flying open-jaw, in to Prague or Budapest and out of the other, would let you travel in a pretty straight line via Vienna. But it may be hard to find a good deal on flights for that route. You may find it works better to fly round-trip with some backtracking by train or a cheap flight between Prague and Budapest