I'd recommend
AMS. A fantastic city to visit, I love going there.
KL and
BE both fly there and both have several flights each way, so can arrive early and arrive back late giving you as full a day as possible. The centre of Amsterdam is only 20 minutes by train from the airport and of course there is all the Heineken you can want! A bit further away but you could do Germany and visit one of the xmas markets. I visited
FRA for their xmas market last year, albeit over a weekend, but with the many flights and only slightly longer journey time, you could do that in a day I reckon. Again, the centre is only a short ride from the airport by train. The only snag would be that the only option would be flying
LH and their fares are typically quite expensive from
BHX (I flew from
LHR, as the fares and fuel to drive there from the midlands was cheaper than flying from
BHX).