I like architectural eye-candy. I second the recommendation for Goerlitz, which can be managed as a day-trip from Dresden, though I hope to return and spend at least one night there so I have a better chance to take it all in.
Another big favorite of mine is Quedlinburg, which isn't horribly far off the path between Berlin and Bremen. It's another town with an incredible number of gorgeous buildings. It gets a lot more tourists that Goerlitz, probably because of its more convenient location. Everything is all spiffed up (which is either good or bad, depending on your point of view). Quedlinburg has a cathedral with a very impressive treasury (Google for an American connection) and a castle. The tourist office runs occasional English-language tours. If the timing isn't convenient, you can rent an audio guide. This isn't a tiny little town. The historic district is quite large. The audio guide took me several hours, and I had already seen the cathedral and the castle. Definitely a full-day sort of place (two nights would certainly not be too long).
Schwerin is also very pretty. It's also not far off the Berlin-Bremen path--but to the north, whereas Quedlinburg is south of the direct route. Schwerin has a nice old town alongside a small artificial lake. And on a peninsula in the lake is a castle surrounded by gardens. Lubeck is nearby. I was sad to run out of time before I managed to see Lubeck. Everyone seems to recommend it.
I adored Berlin, though it certainly isn't especially pretty. Great museums and historical sights. I found the tour of the old Stasi prison very interesting. If the timing of the tour doesn't work for you, the on-site museum has English explanations that impart some of the same information you would get on the tour. It takes a good bit of time to absorb the displays, and the location isn't in central Berlin, so it's not something to take on if you only have a 90-minute gap in your schedule. There are other Cold War sights that are more easily reached.
