Taxis / Car Service:
Legally you don’t need a car seat in taxis and car services, so the ball’s in your court here and though I've done it, I really really don't recommend taking a taxi ride without a car seat. As if a ride in a NYC taxi isn't terrifying enough, this really takes the cake. Sometimes desperate times call for desperate measures, but know that there are several companies that offer car seats and boosters when reserved ahead of time (my personal go-to is Eastern Car Service based out of Park Slope, they usually charge $5 extra for the car seat or booster). There’s also a service geared especially for families called Kid Car.
You’ve got a small selection here, and depending on where you live they may or may not have parking locations convenient to you. But they offer hourly rental, and gas and insurance is included in the price! How awesome! Check out Zipcar, Hertz 24/7, and Carpingo. You’ll have to provide your own car seat, which is required by law.
Not a glamorous way of travel, but cost effective and for the most part, pretty easy. My contention with the subway is the dearth of stations with elevators - check the MTA’s accessible list.
The tough part on the bus is you are required to collapse your stroller. With an infant, diaper bag, and who knows what else you’re lugging around under the stroller, this can be a mama’s worst nightmare. For this reason, the subway wins out in my book, even if you have to solicit help to get up and down the stairs (go here to see which "Subway Mom" you are!)!
Most parts of NYC are pretty pedestrian friendly, so throw on some sneakers and show your little one all there is to see around the city! And bonus, you’ll save some money and work off some of that baby weight while you’re at it! I recommend at least one of the following: a carrier, a stroller, or a leash/harness (if your little one is walking and likes to dart into traffic).
Here in Bay Ridge, we often organize a "stroller caravan" where we walk in groups to meetups such as Babies and Books at the library or open play at Baby/Mama. I think our record was an intimidating lineup of 15 strollers!! We seriously rule the sidewalks in Ba(b)y Ridge!