Originally Posted by
catharsis
Having said that the reason I was trying to avoid taxi's and use public transport was because I assumed our child car seat would be checked through
Are you not using the car seat on the plane for the 2YO? Would advise to keep it with you/gate check it so you can use it in the Uber/Lyft - while not required by law in NYC, it's still recommended to use one. We always use one on the plane anyway for our 2YO so it's never an issue of not having access to it.
Uber isn't "flat rate" per se, but in NYC will show you the total fixed price before you book (depending on current surge/traffic conditions) so no surprises once you get moving.