I think its nice to have a meander. If you have the time and energy, perhaps look at east and west Berlin to compare? You may still get to see an old bullet hole in a wall, although I understand The Wall has been completely removed now.
I live in Berlin and you might want to look for accommodation in Prenzlauerberg which is very clean ( for Berlin!) and family friendly. I don’t recommend staying right in the center as it’s a bit lifeless and Berlin is very well connected. It’s divided into neighborhoods, so you’ll never be far away from some action!