I've spent a lot of time in Germany but never been to the corner that includes Berlin, Potsdam and Dresden.
I'm flying into Berlin, April 25th, with probably ten days to visit the three locations before moving on toward Vienna, Prague and Budapest.
I love anything that connects me to the historical/cultural roots of the people who populate an area (music, food, art, architecture, etc.) Going through the potential sights, I'm finding no shortage of Baroque and Rococo (or Gothic/Romanesque "revival") churches and palaces. I'll certainly visit enough to get a feel for that period.
I'd like to add sights that take me back further in history. For example, major battles between the Gauls and Romans were largely affected by the presence of German cavalry (mercenaries or allies?) on the Roman side. I'd like to know more about Germanic people from Roman times through the Middle Ages. Can you point me to sights that pre-date the extravagant palaces and churches? How far back, in time, does the German History Museum cover?