I had both of my children in Manhattan and we lived there for 3 years with kids and boy can it be a struggle at times with young kids. It is a city that I believe you need to bring your infant car seat, stroller, and carrier. Depedning on your plans for the day decide which is best for you to have with you.
Why you need your stroller? There is a ton of walking in Manhattan and depending on the weight of your child using a carrier all day can cause you major back pain. Also if you are traveling during the peak of summer, using a carrier an entire day can be really uncomfortable due to the extreme heat. Be sure to research which Subways are accessible and have elevators, many times it might make your life easier to get off at the stop before or after your final destination and walk to your destination from there if it is has an elevator rather than to struggle getting up or down the stairs at the closer station with no elevator. Luckily most of the tourist areas are more equipped with elevators but MTA is always under construction and sometimes there is no elevator access at a station that typically has it so be sure to check for updates and travel alternatives here.
Why you need your carrier? For very crowded areas like Times Square trying to maneuver a stroller can be a pain and to avoid unnecessary stress using a carrier in these areas is best. Also unfortunately many of the subways do not have elevators so if you are traveling alone that can leave you struggling to carry a stroller and your child from 2-3 floors underground or praying that some kind strong stranger will offer to help you and not run away with your child.
Why you need your infant car seat? While getting through Manhattan is very easy via public transportation there may be times hopping in a cab is necessary. You may not want to take the train or bus from the airport or you may want to travel to another burrough where taking a car would be easier. If your child can still fit in their infant car seat I would recommend bringing this as you can snap it into a lightweight car seat caddy and it doubles as a stroller. NYC taxi laws do not require a child to be in a car seat while in a taxi but safety first and it's so easy to travel with the infant car seat. If your child is too big for an infant car seat and you find yourself needing a cab you can always use Uber Family and for a $10/fee an Uber with a car seat will pick you up. Be sure to research the type of car seat Uber provides as it is not a traditional car seat and some restrictions apply.