Grand Central Terminus (not 'station' as it's often wrongly called) is well worth a visit - do the audio tour!
Top of the Rock is more impressive than going up the Empire State in my opinion, because you can see the Empire State building from up there.
MoMA is fantastic if you like Art.
If you can stretch to it, a helicopter flight around Manhatten is also.....Awsome!
Keen's steakhouse is v good:
https://www.keens.com/
And if you're around Wall St this bar and restaurant is also excelent:
https://www.harrysnyc.com/