We just did a 2 night stop-over on the way back from the UK at the beginning of January! We stayed at the airport because we didn't want a mad rush the morning we were flying out and had loads of luggage that we didn't fancy carting on the train to downtown! So I can't really comment on where would be good to stay nearer to the center. There are regular trains direct from the airport into the center, takes about 30 mins. We got a 2 day travel card for 20 euro which I think covered all Amsterdam trains, buses and metro. The metro was very useful as it was very cold and windy so we didn't always have to walk everywhere!
We were quite short on time so didn't do much other than walk around the streets and canals, which is what we like doing anyway! Had the weather been nicer we would have spent much more time just mooching around but were back at our hotel by 5 pm both nights. The one tourist attraction we did was the Anne Frank House Museum. I found it really interesting and quite, I don't know if humbling is the word. However, dd was bored and this made it slightly stressful when everyone was being quiet out of respect and she just wanted to run around. In hindsight I'm not sure we should have taken her there. We also visited the flower market on the barges (I forget the Dutch name). I really wanted some tulips but the ones that were certified for import to North America were all the normal colours and more expensive. I really wanted some black tulips! We did manage to bring back some cheese though! The cheese shop we went in gave us loads of samples of different cheeses to taste - unfortunately for dd she was asleep so really missed out there!
Not sure what else, I'm sure someone else has spent more time there and will have more information

Edit: sorry, just re-read and sounds like you are driving? In which case ignore everything I said about trains!