How far can you travel?
I used to live there, and closeby you can find the following:
The Leidse Hout (between Leiden and Oegsgeest) always had wintering Firecrest (some searching will be required!).
The Hortus in the heart of Leiden was my usual location for adding Tawny Owl to the year list (nothing else though!)
If it's really cold and everything is frozen (hasn't happened in 10 years...), the northern side of the old town and the canals north of there can be good for ducks (even had Scaup there!)
Public transport would take you to the following places within 30 minutes:
The mouth of the river Rhine in Katwijk can have some interesting gulls (but usually doesn't). I like the dunes a lot more: a bike ride between Katwijk and Scheveningen (schedule 3 hours round trip) can be worthwhile if only for the landscape. There has been a lot of reconstruction of the dunes... good for plants, not so good for birds! Smew and Red-crested Pochard should occur south of the Wassenaarse Slag (no public transport in winter).
The area south of Leiden can be good; check this map:
http://www.vogeldagboek.nl/Natuurkaart.html
Starrevaart (left on the map) near Leidschendam (a short walk from a bus stop in Voorschoten) is full of ducks (incl. Smew) and usually has Bittern and Bearded Tit (good luck!) Rarer birds occur regularly – a well-watched site. The polders east of the A2 motorway are excellent for Great Egret: De Wilck (lightblue, centre) would be a good place to start. Also Bewick's Swan there, and Peregrine has wintered there for years.
A good area for geese is north of Koudekerk (upper right on map).
Scheveningen harbour (1 hour by public transport) has Purple Sandpiper without fail.
With some luck, Little Buntings will return for their third consecutive winter in Katwijk. Keep me posted (by pm) and I'll give you the latest updates!
http://waarneming.nl (sightings of just about anything) can be watched in English, but it may be hard if you don't know all the local places.