Thanks, we actually went on 2nd Jan. It was MOBBED!!
We went to the Anne Frank House - knowing in advance about pre-booking would have saved time alright. The queue never died back from at least an hour long anytime we passed it (and we went pretty early in the morning). It was well worth it though - very very deep and sobering (I had read the book before as a teenager, DH hadn't).
We saw the Van Gogh exhibition in the city centre (not out to the VG museum) which was really interesting.
We took a canal boat tour at dusk (5ish) so enough light for photos for 1st half, and then enjoyed the dark and seeing the city by night from the canal. That was good timing.
When we rented bikes, we went out from the city centre to the parks and more residential parts of the city - which was really interesting, especially the differences between the 2 areas. (We stayed right in the heart of the city).
We also did a lot of walking both day and night.
Public transport looked great (trams etc) but we didn't need it.
We only had brownies in the Anne Frank House, so regular ones. But the "non-regular" type were obviously freely available in parts.
We were exhausted by the end of it, as we kinda went back to pre-child days of city breaks (see everything possible in 3 days and rest up in the following week) without remembering the lack of rest possible. And the cabin pressures were messed up on the descent coming home (not just me and DH, loads of people had problems) and a Christmas cold didn't help that (I never have ear problems but I had tears rolling down my cheeks with it).
Otherwise, it was well worth going to!! 
As for weather, very like here, grey and dull mostly, and 1 day there was a cold wind, but temps very close to here too (7-10ish) - but we had thermals in case. Some interesting shops too (not all UK high street stores - check out "The 9 Streets" for interesting boutiques etc).