We've just come back from a couple of days in New York. If you are at all into the theatre I can't recommend The Ferryman too highly, saw it last night. Get half price tickets, for that and many other shows in the booth in Times Square.
Do not, what ever you do, go to Perfect Crime, which is billed as the equivalent of The Mousetrap in London, the plot is hopelessly convoluted, opaque and ridiculous and the acting, particularly the lead who has been playing the part for over 30 years, is dire. I've seen far better school plays. The Mousetrap is a well produced and acted play, Perfect Crime is a crime against theatre goers.
Definitely walk the High Line, also visit Chelsea Market which is at the southern end of it for a huge selection of interesting food. There is also a little makers' market there selling jewellery etc which is interesting. The Warhol exhibition may still be on in the Whitney in April, be aware the Whitney is closed on Tuesdays, which we did not know the cafe in the Whitney is very nice. Many Broadway shows are on on Sundays but off on Mondays.
My late teens DD really enjoyed having a coffee in Ralph Lauren's coffee shop just off Madison Avenue (Ralph's), very classy and quiet and very friendly. Good Instagram opportunity, if that is your thing. We also visited the Glossier makeup store, which was her favourite thing (it is a very nice shopping experience). Also Instagrammable, I'm told.
Personally I think Times Square is hell on earth but it is a spectacle, it was much better this time, in February, than it was in August when it is just too hot, too seedy and too crowded.
We enjoyed the Hop-on-Hop off bus tour, buy online before you get on. You can get bike hire in Central Park included, which would be fun I think.
Finally keep an eye on the weather forecast, it is usually fairly accurate a few days ahead, the last few days were unseasonably hot in New York but April could also be unseasonably cold!