Berlin in Jan

Hello, i have been reading through lots of posts on here, but there is so much info about all different things!!

I am looking to take my boyfriend as a city break for a birthday present.

This would be 21st to 24th Jan.

Is this a good time to go? or does it not really matter what time of the year?

I am aware that it will most likely be cold, which is fine.

I just want to have a nice romantic getaway, see some of the sights, eat out etc.

Also, i have been told that Charlottenburg is a nice place to stay? But i havent a clue, when i looked there at a hotel it was next door to a strip joint! Im not a prude, but as its a birthday gift would like to stay in a nice hotel for my budget.

I notice there are a couple IBIS hotels which are well priced.

Any pointers would be great as at present i cant decide between Berlin or Budapest.

Either way it will be bloody cold!! :)