Making first trip to Prague, was thinking about going to Dresden and Berlin also - any suggestions?

How long are you planning on Dresden/Prague?

In Dresden:
Frauenkirche
Zwinger Museum - It is really cool with not only art.

Berlin:
San Soucci Castle
Checkpoint Charlie Museum
Stasi Museum
Brandenburg Gate
Main Art Museum
Try a curry wurst - bratwurst with curry
Doener Kebab - They are good and cheap

Are you driving? We left Prague and took a night to make a loop east to Kutna Hora, then north and back west to Dresden. Two nights there and then a night to loop kind of west back down to Prague. Many of the places we stopped the locals acted like we were the first Americans they had ever seen. Little town of Oybin, Germany was really cool. Saxon Switzerland was nice, The armoury museum in Dresden is one of the best in the world. I can give recommendations on food and lodging if needed.

We did a day trip to Cesky Krumlov. If I remember correctly, it was about 2-2.5 hour drive each way. It's a neat medieval town.

https://www.ricksteves.com/watch-read-listen/read/articles/cobbled-charms-of-cesky-krumlov

If you are into german military history, the Dresden Military History Museum is a great visit.

if you haven't been, consider Budapest. I thought that those two cities paired well together.

Berlin:

Curry 36 for the best currywurst imo

Tempelhofer Feld is the old (now retired) airport for basically the entire 20th century and is now a park that does tours if you book on the internet.

Museum Island

Alexanderplatz sometimes has stuff going on

Walk the wall on the former East side of Berlin near Ostbahnhof

Buy beer from a corner store and walk around with it, you can find some good stuff for about 2 euros a pint.

KaDeWe (Kaufhaus des Westens) near Zoologischer Garten and the old bombed out church if you want to see the biggest shopping center you've ever seen with some really cool stuff in it.

Potsdam is cool, as are a lot of other places like Wannsee southwest of the main city along the train line.

Great feedback, thanks everyone. We plan on taking a train and have 5 days to spend in addition to Prague.