I am writing again, I love Vienna, Prague and Munich in that order. Not to say you may love those cities in a different order.I have not been to Berlin or Budapest but as you know they are very much wonderful cities.Since you are already in Munich you may want to stay in Munich and see it. Why move around so much when you are already in a great city. Do get the guide books on each city, you can watch free videos of Rick Steves and other travel shows on YouTube. You can also look on this website there is are on line scrapbooks of the places you want to visit. Seeing is worth 1000 words as they always say.
In Munich you can go to St. Michaels Church, St Peter's Church, Nymphenburg Palace, The Residenz ( the city palace), The Alte Pinakothek (14th to 19th Century) art, Neue Pinakothek ( I loved this museum), Asam Church, tons of beer halls, Frauenkirche church, Marienplatz, BMW musuem, Dachau Concentration camp to name a few places and things to see and do.
In Vienna, St Stephen's Cathedral, Kunsthirsorisches Museum ( amazing museum), Hofburg Imperial Apartments, tons of wonderful cafes, Belevedere Palace ( where The Kiss is by Klimt), Karlskirche church ( looks like a church that should be in Rome), Albertina Museum, Hofburg Treasury, Schonbrunn Palace, tons of concerts, and many other museums.
I love Prague, but it has been several years since I visited. But there are tons of sites, places to visit and great beer.
No matter what you pick, it will be amazing and fun and interesting and different that the US!
Have a great time.