We went last December, just for the Christmas markets and a bit of walking around, we had 3 secondary school age children with us so it was Friday pm - Sunday pm only.
It was cold, below freezing and there was still a bit of snow around as well. Be prepared to wrap up warm.
The best market was the one near the Rotes Rathaus (red town hall) and what is normally on the Gendarmenmarkt (it was relocated due to building works), a lot more upmarket but nice items, they had tents as well with cafes to sit down.
We are currently here again, 33 degrees today.
There are more museums than you can think of. Some at the Museum Island are currenlty closed for renovations, make sure you double-check their websites.
We just went to the DDR Museum, DH and I are both German, we were teens in the 80th and have family connections. We found it very confusing, very busy and not that organised. Saying that, our 17 year old DD found it very interesting.
You can book a space to go up the dome in the Reichstag, it's free but a bit complicated to book, make sure you go via the offical website.