K.P.
First suggestion would be to take the train if possible. Parking in and around the City is tough on a regular day, let alone a holiday.
Second, bring your stroller with the detachable car seat. That way you have mobility and can use a cab safely. The driver will put the stroller in the trunk.
Third, wait another couple of years to do this. The City at Christmas is beautiful, but in all honesty it is a lot to try and do with small children. You want to see the "sights", you would want to see...
- Radio City Christmas Spectacular
- Rockefeller Center Tree and skating
- Toys R Us (used to be FAO Schwartz)
They are really short cab rides apart, but do your research and make sure that this is something you REALLY want to try with an infant. It will be cold and windy with potentially long waits and periods of sitting still.
If you do decide to do this, go on a week day and in the morning. Have a sheet with you of the addresses you will need to find as well as a train schedule. Because you don't know where you are going, don't attempt the subways.