H.U.
Hi there. I'm a native New Yorker with a 2 1/2 year old and I travel extensively so I hope I can help you.
How old is your baby? I used a carrier like this up to when my son was about 12 months old (the Peanut Shell). More for the plane or train or rocking him to sleep at a friend's house not so much for walking around outside. I used the Bjorn for walking around. After that we switched to an Ergo carrier - more like a fabric backpack where you can carry the baby on the front, hip or back. Both the Bjorn and Ergo are much more secure and balanced. In fact I still carry my son in the Ergo on the days when I take the bus and don't bring the stroller. I'm not sure how comfortable this hip carrier will be for you. I would recommend either the Bjorn or Ergo over this hip carrier.
That being said, is there no way you can bring your stroller? You will be walking A LOT in New York and carrying a baby for many days can be really tiring. Strollers in NYC are our minivans and SUV's - we live for them. I've brought my Bugaboo all over the world (which as you know is a massive stroller) and I've never regretted it.
Here are the rules for public transport - no strollers on the bus. If you do bring a stroller, you must fold it up before entering the bus. You can bring a stroller into the subway. Take a look on the map mta.info for the stops with elevators (marked with the handicapped accessible sign of a person in a wheelchair). They are usually the most popular stops - 42nd Street Times Square, 34th Street, 14 Street, Union Square, etc. Other times you can just ask someone to help you carry the stroller up the stairs. I do this less frequently - I'd rather get off at a stop with an elevator and walk further, but that's me. So many of my mom friends just ask for help and people are always happy to help you - the same for me when an elevator is broken.
I don't believe museums rent strollers. In fact, there are some with anti-stroller policies, such as the Children's Museum of Manhattan. You can bring your stroller there but you have to check it before you enter. Here's a link to a great resource to help you plan your trip to NYC with children mommypoppins.com. It's a list of museums and their stroller policies - http://mommypoppins.com/ny-kids/stroller-policies-at-new-...
I hope this helps! Have a great time in NYC.
H. Ureña Black (mom to Christian Black)