I went in April last year with my mate, and then in Dec with my ex missus ( )
So, with a little experience I particularly enjoyed the following:
Central Park is a must!! Especially this time of year as the ice rink will be open, you can laugh at one another face planting your way around (hopefully not, btw)!!! There is also a zoo in Central Park, which is pretty good.
East Village is a nice, cultural part of Manhatten, good shopping round there, too, in my opinion, anyway.
Plenty of good shops and restaurants on 5th Avenue between 34th and 59th Street.
Also, I would say to go up The Empire State Building at night. To see the overview of NYC lit up at night is nuts!
Hope this is a little help to you.
Have a very good trip!!