If you've abandoned the RV idea, I think you might have the one situation where I would consider just renting a car in NYC.
You will have to deal with traffic and tolls as well as parking, however, I could see when traveling with an infant that having a car nearby, even if just as a place to put your stuff, could have some advantages over having to lug around a diaper bag everywhere.
If you go that route, I'd download a parking app, like SpotHero that can help you find more reasonable parking rates, especially in urban environments.
For renting the car, I'd look at picking up in Newark. One way rentals often have to start at an airport, and not only is Newark on your way out of town, unlike JFK or LGA, rates and taxes in New Jersey can be less than in New York.