Mid-May is beautiful in the city. At her age, yeah I’d pass on anything longer on the open water than The Circle Line and agree that the Statue of Liberty will be completely lost on her. A cool damp boat ride and not much more.
2 year olds nap. The Libraby is beautiful, the museums are great and warm, quiet places. If you hit a very warm day and you think she’d tolerate it ( and you are a sports fan ) buy cheap seats to a Mets or Yankees game, just make sure you’re sitting on the sunny side of an afternoon game. Might be exciting for her. Till she falls asleep, of course. 
My babies rode the NYC subways. I took my 6-month old son into Manhattan from Astoria the DAY after he arrived from South Korea. They rode for a year or two till we moved out of the city. Their hearing is fine. The thing about the subways is that they are startlingly LOUD and sometimes there are screetching sounds that might scare her. If you are worried, and can make a game of it, buy two sets of ear muffs from Home Depot. They’re about $ 13.00 each. They will be amusingly oversized on her little head, but will cover her ears well enough and she can laugh and see you wearing yours. Or… you can let her hear the train sounds.
Grand Central Terminal is quite lovely and has huge open spaces to let her walk around in. There are playgrounds on the Lower East Side below Houston Street that are neato. Also great ones in Central Park. Here is a listof all the playgrounds in Manhattan.
I would also seriously recommend The Chelsea Piers. It is a huge sports complex that is on the Hudson River. Google it, take a peek around. There might well be an activity you can take her to where she doesn’t have to be an enrolled attendee. From babies to oldsters, there are things there for folks to do who like to run and play.
Travel times by bus or subway are largely irrelevant to a child that age. As I said, I TOOK a 2 year old all around the city. Long ride out to Coney Island Zoo, or a ball game, or wherever? She’ll fall asleep with the gentle rocking of the subway cars. Yeah, they sometimes slam around but mostly it’s good enough that you will see plenty of other babies in strollers asleep.
Oh- the stroller thing. Different NY Dopers will have different things to say about this. Here’s my take. I’m a pretty big fellow, and had no trouble lifting a front and back double stroller up the stairs. I almost ALWAYS had people offer to lend a hand, and it is considered good form as a subway rider to offer to help carry even a single child stroller up along with the parent.
On the infrequent trips into the city now, if I see a stroller user approaching the stairs, I stop and ask. You will likely have offers like this everywhere you go, both in Manhattan and in the outer boroughs.
I’m not a native, I grew up in Philly but have lived in NYC and the surrounding areas since 1981. I can tell you honestly that the bad rap NY’ers have is almost completely without basis in reality. People lend a hand, give good accurate directions and smile more than you would think.
The Children’s Museum of Manhattan is great, and on the Upper West Side.
Similarly, The Children’s Museum of The Arts in lower Manhattan is just a blast for toddlers. It has famous art- and thousands of pieces of children’s art BY children. Quite something.
When you hit town, go into one of those dreadful touristy stores and buy the thick laminated map of the NYC Subway System. It’ll come in very handy during your stay.
And have a blast !!!
Cartooniverse
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