Help w/ Berlin, Prague and Black Forest planning

I assume you're talking about the Black Forest in the far southwest of Germany? It's too far away from Prague and Berlin.
The Saxony Region and Dresden, Germany would be the preferred stop between Berlin and Prague. Dresden now has around 800K people, and it's being restored to be one of the most beautiful cities in Europe. It has what you're looking for.

Due east of Dresden (but you'd need to go back to Dresden before traveling to Prague by train) is the lovely town of Goerlitz. It sits on the Polish border. Goerlitz survived the war basically intact and has lovely architecture from many eras from medieval to early 20th century. A great deal of restoration has taken place since the wall came down, and the city is often used for location filming. Because it is in a sort of forgotten corner of Germany, it doesn't get very many foreign tourists.

Hi,

Where in Berlin does your son live? In which district?

If you're entertaining logistically feasible day trips by train from Berlin, then I would suggest Dresden, Meissen, Leipzig, Halle,

Naumburg an der Saale, Weimar, Schwerin (depending on the connection), Lutherstadt Wittenberg, Magdeburg,

Lots of culturally and historical small places too...Neustreltiz, Jena, Wustrau/Brandenburg, Neuhardenberg, Rheinsberg, and of course, the obvious, Potsdam where an entire day can be spent visiting the famous chateaux/Schlösser, museums, taking boat ride, exploring the outside of the Zentrum, etc.

Drop the Black Forest. It is out of your way and there are so many places nearer your route that are far more interesting and beautiful. Dresden is being suggested by many, and I agree.

David - Dresden has a population of only 540,000, not 800,000. If it had 800,000, it would be the 5th largest city in Germany which it isn't.

You have a lot of time to explore very different places and sights of Berlin, also smaller ones. As foodie try a week(end) market or streetfood Thursday at Markthalle Neun or Tajikistan tearoom.

Close to Berlin the palaces of Potsdam (filter by click on Potsdam) are a must have for your interests.

City of Dresden had "only" 543k residents counted in 2016 but I agree that it is worth a visit. I also agree that Saxonian Switzerland is definitely a much closer option than Black Forest. Altenatively Ore mountains (shared with CZ) or Harz are comparable experiences but better kept secrets to US travel industry. Especially Harz towns Quedlinburg and Goslar are extremely pretty and UNESCO world culture heritage. Mountain Brocken is one of favorite places people in northern part of Germany want to visit. Also Harz steam engine narrow-gauge railway is a beloved experience. Do not forget to taste Harz Cheese.

Speaking of cities: Erfurt is easy to reach by train and a beauty. Eisenach and Wartburg are close.

Furthermore Hamburg and Lübeck are really worth visiting. Also very different to Berlin in culture, food and architecture.

If you absolutely want to do far away Black Forest you can get there by night train NJ 471 from Berlin to Offenburg or Freiburg: https://www.nightjet.com/en/reiseziele/schweiz/basel.html

As already mentioned: the Black Forest is too far away. But the Black Forest, and the Alps, are hardly the only mountains in Germany. Halfway between Berlin and Prague are Saxon/Bohemian Switzerland, the Ore Mountains and the Zittau Mountains.

Saxon/Bohemian Switzerland are the most convenient, and the most spectacular mountains. They are a easy day trip from Dresden (40min), and hiking there is really a great experience.
The Ore Mountains are less spectacular, but in terms of culture and traditions they are very interesting. Everything there is related to mining. Later these miners turned to woodcarvers, they began to sell their products on Christmas markets, and today the products and (mining) traditions of the Ore Mountains shape German Christmas, which means the mountains are THE German Christmas country. Even in the summer.
The Zittau Mountains are the smallest of the three. Picturesque, in a very traditional and remote region, with some of the cutest villages of the country, with hundreds of so called Upper Lusatian Houses.

All of them are in the vicinity of Dresden, but for the Ore and the Zittau Mountains you need a car. Dresden itself is a great base for day trips to castles and palaces, picturesque towns and villages, vineyards and wine villages etc.. You can easily spend a week there.

I'd listen to Mark and Martin here. The Black Forest is lovely enough and worth a few days if you're already going to be in Southwestern Germany/Southeastern France/Northern Swizterland but otherwise I don't think it's interesting enough to travel across the country (even with the amount of time you have) when you have better options much closer.