I just came back. I was born there and go at least once a year. That time of year NYC is crowded, don't worry, I mean that's part of NYC. Saying "avoid the crowds" is like saying go to Hawaii but avoid the beach because it will be crowded.
Weather can impact your plans. if it's nice you can walk over the Brooklyn Bridge and go to Grimaldi's for pizza. It always has a line so go around the corner to Ignazios, I think that's the spelling. Take the A line subway back. The bridge can be crowded but it's free, gives great but distant views of Statue of Liberty.
The Staten Island Ferry is free, goes close to Statue of Liberty.
Go to Saint Pat's on 5th Ave. It has the most amazing stained glass in the country-maybe the world. Great building, I always go and light candles.
A walk around Central Park is solid.
I saw, "Come From Away" this time. A great play/musical about the town of Gander in Newfoundland and how they welcomed and cared for people on dozens of planes that
were forced to land there on 9/11. Despite the subject, it's a fun, uplifting show.
Getting around? Subways. That can be a wild ride. Crowded, characters, confusing at times, but cheapest way to get around. Cabs charge while you sit in traffic, frustrating.
Get a map and a subway card.
If the weather is OK, the Gray Line tour around Manhattan- 3 hours-is touristy, and costs money, but informative and you see many things.
People go to NYC and embrace all that it is, or they're put off by it and waste their money. Understand it is different, crowded, but in all the years I've lived or gone there, I've never seen a fight, bullying, abusive cops, or really bad scenes. Be prepared for difference, crowds, people pushing and shoving at times-think subways.
I hope you have a good time and please post about it when you return.