After Prague - Eastern Czech Republic or Eastern Germany

The train is fast and easy, Prague to Dresden, then Dresden to Berlin. Potsdam is a day trip from Berlin. Berlin is a city of contrasts, with lots to see and do. I would not pass up an opportunity to see it.

Krakow to Budapest would be a good auto trip if you want to see Slovakia, but you'd have to check if there are any restrictions on driving a rental from the Czech Republic across borders and what the drop-off charge would be to return it in Hungary - or would you drive a loop and return to the Czech Republic? It's about 7 hours driving time (not including pit stops) from Krakow to Budapest. The best way to travel between those 2 cities is by car or bus. There are no direct trains or flights.

I would appreciate suggestions for the best towns to visit in Czech
Republic and Eastern Germany.

How many days, and what are your interests?

And also it would be good to know when; what month?

Thank you for the information, especially about the no direct trains and planes from Krakow to Budapest. That will be more of a challenge. I haven't researched that far ahead.

We can spend about fifteen or sixteen days in Europe; a minimum of four nights are necessary in Prague because of business. Is there a lot of variety among the small Czech towns? They seem to change as you travel further east – more of the wooden churches, etc. I have very little knowledge of the Czech Republic and am depending mostly on guide books and the internet.

I forgot to mention that we will be in Prague the second week in September.

I would appreciate suggestions for the best towns to visit in Czech
Republic and Eastern Germany.

Eastern Germany is actually pretty big. Touristically you can divide it into:
Saxony
Thuringia + "Lutherland"
Harz mountains
Baltic coast
Berlin + Potsdam

Saxony bordern on Czechia and is touristically the most diverse region, with everything from world-class museums (Dresden), beautiful historic towns (Görlitz, Bautzen, Meissen, Freiberg etc.) and cute (wine) villages (suburbs of Dresden) to castles, fortresses, picturesque mountains (Saxon Switzerland) and interesting traditions (Christmas in the Ore mountains).
Thuringia and "Lutherland" are between Saxony and Western Germany. This is basically Small-town Germany + Luther + Wurst. Erfurt, Weimar, Wartburg castle, Naumburg, Wittenberg, Schmalkalden, Rudolstadt, Gotha etc..
The Harz mountains offer several perfectly preserved town with literally thousands of half-timbered houses (Quedlinburg, Goslar, Wernigerode, Stolberg, Wolfenbüttel, Einbeck...). If you want to see a Rothenburg odT without the tourist hordes and trinket shops go there.
The Baltic coast is Germanys most popular summer destination, and not just because of the great beaches but also because of the 19th century "spa architecture" of many resorts (Binz, Imperial Spas) and the preserved Hanseatic towns (Lübeck, Wismar, Schwerin, Stralsund).
Berlin is the modern metropolis that never sleeps, nearby Potsdam the opposite... the hideaway of the Prussian kings for 200+ years.

You could mix big city (Berlin) and small towns or beaches and nature, you could hike in Saxon Switzerland (google for pix) and do day trips to all kinds of places, you could rent a car and see a bit of everything....

You mentioned that you would be in Prague second week in September. September 10-11th there is the biggest folklife festival in the country in Uherske Hradiste (about 3 hours drive from Prague). I don't know your interests but IMHO it's certainly worth to visit. Saturday morning there will be a parade of several thousand people in folk costumes from different villages in UH region accompanied by folk music bands. A lot of food stands, wine stands, traditional art stands, etc. The performance will be all over the town. You could also visit wine cellars in Vinohradska street in neighborhood Maratice. There will be short river cruises with bands on the deck of the ships. If something like that interests you then book a hotel right now. The best is hotel Slunce then Grand (it's Best Western and it has a gated parking), hotel Mlynska, hotel Maxi. There are many more if God forbid those would be already taken.
Here are some websites which could help with your decision:
http://www.slavnostivinauh.cz . You can switch it to English. Unfortunately not all of it is translated.
http://www.youtube.com/watch?v=7mAeml3xKGw
https://community.ricksteves.com/travel-forum/czech/favorite-destination-in-the-czech-republic
After that you can drive to Brno (about 1 hour), the second largest city in C.R. with plenty to see and do. On the way there you can stop in chateau Buchlovice (it has a huge beautiful park) and castle Buchlov. In Brno you can visit St.Peter Cathedral, castle Spilberk if you are into history - Austerlitz battlefield and museum, villa Tugendhat (functional architecture gem - it's on UNESCO list). I recommend - book the visit now. There is a huge interest to see it. Request tour in English. You can also take a boat ride to Veveri Castle on the Brno Lake. From Brno you can drive to Trebic and visit Jewish Ghetto. More in R.S. book. Then Telc with a picturesque fairy tale square. Also in R.S. book. Jindrichuv Hradec - chateau and pretty square. Trebon - see R.S. book. There is a large lake called Svet (which means World). We rented bicycles and did the journey around the World (about 12 km). Then Ceske Budejovice - historical regional town; German name Budweis and yes, you got it - that's where the original Budweiser is brewed. IMHO much better than the one from St.Louis. You can take a tour in English. And then the cream of it all - Cesky Krumlov. See R.S. book. On the way back to Prague you can stop in Tabor - founded by religious rebels Hussites. There is a Hussite Museum in Tabor worth visiting. Then castle Konopiste (next to Benesov) also in Rick Steves book: Prague & the Czech Republic. All of it is of course doable by public transport, too.

Hi,

There is the night train option, a direct link, from Krakow to Budapest.

On Eastern Germany: I was there a good deal of my last trip a few weeks ago, very nice, enjoyable. Culturally and historically I would suggest Naumburg an der Saale, Potsdam, Halle , Magdeburg, Meissen, Leipzig (esp if you're into classical music), Jena (for science and the battle ), Weimar (on German literature), Frankfurt an der Oder (if you want to see a city not visited any tourists), Dresden, ( for day trips to Schloss Pillnitz), If you speak German, it's even more enriching traveling and exploring the cities and towns.

Do you intend to get a rental car? Traveling by car through those villages in Brandenburg, seeing that landscape won't be anything comparable seen in western Germany, eg, going northwards from Berlin to Greifswald or Schwerin, or going east ward to the Oder River.

Take the train to Berlin. I only suggest renting a car if you intend on going out to villages in the Greater Berlin area, or to the villages/town in Brandenburg, such as historical towns Rheinsberg, Neuruppin, Seelow (on WW 2), etc, etc. Any particular interest?

You realize of course that a flight from Prague to Budapest is less than half the cost of a rental car from Krakow to Budapest. Half the time too.

"...if you're into history Austerlitz battle field and museum." The museum is located in the town of Slavkov (Austerlitz) in the chateau ca a 40 min walk from the Slavkov train station at the beginning of the center of town (Zentrum), called "Napoleon Exhibit." You are guided through each room but left to yourself to see the displays, etc, took me one hour to see the whole thing, ie, each of the exhibits, very well done, in Czech and English, balanced and thorough in its treatment of the Russians, French and Austrians. ... very well kept up, the whole thing used to be called Schloss Austerlitz bei Brünn..

Fred is right; there is another museum in Slavkov chateau where the armistice between Austria and France was signed in December 1805. The one I mentioned is on Prace Hill adjoining the Cairn of Peace Memorial. You can get there by municipal bus #48 from Brno or you can drive there.
http://www.mohylamiru.muzeumbrnenska.cz/en/

@ Ilja...That's correct. In a way I sort of bumped into the chateau in Slavkov walking from the train station. You see the chateau and the immediate surrounding area just prior to entering the center of town (Zentrum). Big sign indicating the Napoleon Exhibit. I was looking for the monument at the Platzen Heights but didn't know it was there, until I saw a photo in the Exhibit of some local event showing that monument, which I recognised as the one I wanted to see, and asked where that was. The Czech woman attendant said, "Prace." Yes, I see, the Pratzen Heights in English, or as know then in German, Pratzen Höhen. Well, I learned something, seeing that site will have to be next time.

That armistice with the Austrians led to the Peace of Pressburg by the end of Dec 1805. Napoleon should have offered more lenient terms.

Note that Cesky Krumlov is, alas, not very close to Prague. There is a lot to East Germany, including Bach, Luther, Zeiss, and Goethe. I trust you know that Berlin is the most visited city in Germany, and not a relic of Ostalgia! Anyway, consider Dresden, Leipzig, Erfurt, Eisenach, and Quedlinburg, among many others. I don't care about cars, but we went to see Zaha Hadid's BMW plant from the outside.

I think Eastern Czech Republic may also be very scenic. See the fact-based fiction film "Zelary".

@Fred: in Czech the neighboring village is called Prace (read Pratze). I was however able to google Platzen Heights and also Pratzen Heights. So I don't know if that Czech woman could not pronounce "r" and said "l" instead or if both names were used in the past.

sorry...I misspelled it. What I saw on the photo was Prace. and also Pratzen Heights is the correct spelling

The maps at the time show the surrounding villages, Tellnitz, Solkolnitz and Austerlitz and the Pratzen Höhen.