Prague, Vienna, Budapest - what order?

Either that order or the reverse order would make sense. Add a day to Budapest, if you can, maybe taking it from Vienna.

Going north to south and west to east, you’ve got the right order. If you haven’t booked flights yet, do you get the best deal flying to Prague and home from Budapest? Or would reversing that give you cheaper rates and/or a better flight timing?

Whether you return home from Prague or Budapest, you'll have to go to another European gateway airport to return to North America.

I would save Budapest until last.

If you are making no stops in between, since I am no great fan of long train rides and would prefer to save about 4 hours of travel, I would:

Fly from Prague to Budapest and then train to Vienna. (Or reverse). If nothing else, considering it gives you another option for the final departure city when checking costs. This doesn't always work, don't compromise on your schedule if the flight doesn't line up right.

https://community.ricksteves.com/travel-forum/czech/prague-to-budapest-transportation-options

What time of year? As a general rule work north in Spring to have the best weather. Fall, work south. Summer, hot and crowded either direction. That said, I'm visiting these cities, plus Berlin, this Spring and decided to start in Berlin - because I was getting better flight deals and generally cheaper lodging in late April than late May.

These are perfect destinations for using a train. Between Vienna and Budapest, make a day stop along the way in Bratislava for a walk around the old center and lunch. Between Prague and Vienna, stop in Brno for the same.

How much time for each? Research the sights you want to see in each city, then decide. Vienna offers a wide selection of grand palaces, museums, operas, galleries, homes/birth places of famous composers and more. If those are your main interests, five days may not be enough. The same for the other cities, you may want to spend more or less time in each but decide based on whether the sights are interesting to you.

Hello from Wisconsin,
5 days per city sounds reasonable to me.

The order? That is a really good question. The comment by one responder about when you are going. The latitude difference between Budapest and Prague is pretty small, like 150 miles, 2.5 Degrees latitude. However, at their latitude of about 48 degrees N, 150 miles does make a difference especially in spring.

But the cities...Budapest is a real city where tourists mix with the business of the day. Modern buildings mixed with structures from the Austro-Hungarian era. Vienna and Prague probably share more architecture with Vienna being more majestic. Prague is jaw dropping pretty.

enjoy, no matter what.
wayne iNWI

The weather is too unpredictable, and if you look at the averages for each city there really isn't much difference between them; I would look for events or special events or activities on certain dates and plan around that .... and airfare cost.