Your itinerary should be a factor also of how cheaply you can fly into one city and out of the other - where do you want to end up to fly home - ois a return flight to Munich much cheaper than flying into Munich and out of Budapest - the best scenario I can think of:

Munich - Prague - Vienna - budapest.

For trains check out these super informative sites IMO - www.seat61.com; www.budgeteuropetravel.com and www.ricksteves.com. There is a Eastern European Railpass valoid in Austria, Czech Republic, Slovakia and Hungary (and Poland) that could be a good deal if you want total flexibility to hop any train anytime and especially if you desire first class over 2nd class and its IME many benefits for the average tourist hauling around way too much luggage.

Otherwise scour the sites of various national railways for discounted though usually severely restricted (train-specific) tickets that are often sold in limited numbers and which often must be booked weeks in advance to get.

The best way to Prague from Munich right now is by bus direct to Prague - quicker than the train.

Check out the cost implications of doing an Open Jaw flight itinerary: Arrive Munich, depart Vienna. The Munich Prague bus is an excellent idea. Then probably Budapest, last Vienna. If you can't get an open jaw, you can get reduced fare rail Vienna- Salzburg, and a Bayern ticket Salzburg- Munich (airport) The latter costs EUR22 for one person, EUR 26 for two. Yes, I know Salzburg is not in Bavaria, but you can get that ticket there, at the RR station. Earliest departure 9AM on weekdays; only Regio (local) trains, but on that 2 hour route it makes only a difference of about 1/2hrs. Check www.bahn.de for train schedules in any of these countries you plan to visit.

Thanks so much for the tips, PalenQ and treplow! I checked and it would be cheapest for us to fly out of Prague, i.e. fly in to Munich and fy out of Prague. Given the locations of the cities, do you think this travel order makes sense -- Munich - Vienna - Budapest - Prague ?

Yes that order makes sense to me - there is an overnight train linking Budapest and Prague - it is a long day train - save travel time and the cost of a hotel by talking the overnight train.

Yes, I agree with the sequence.

Going from Budapest to Prague you will probably pass through Vienna. See our similar trip in 2011 - http://www.rimerson.com/

Rob

Thanks again, PalenQ! Very much appreciated.