On a budget, Berlin Wall Memorial (Bernauer Straße) still earns its price.
Free
This is where you actually understand the Wall — a preserved death-strip with the original fortifications, a viewing tower, and stories of the escapes and deaths right on this street, all free. The catch: it's an outdoor stretch in a less-central area, so it takes a deliberate trip and is best with the (free) audio or guided context.