Train. with car seat and snap and go.
You can take cabs in NYC or take the subway. My parents Live in NYC. I have done it more times than I can count. Get a red cap and board early. It is the no stres way to go. Rarely delays so travel time is more predictable than driving.
Have fun

Train. .

Train for sure.

I vote for train. I've never been there, but my husband has. NYC in January is going to be freezing. You don't want to be strollering around outside too much, do you? I'd stay near where you're going to be, and don't try to do too much. I'm exhausted just thinking about it.

Drive so that you can carry all of the crap that babies need.
Park the car in a garage and walk or uber everywhere.

We always drive and park too.