I strongly suggest an organize walking tour.
There are a huge number of hidden gems you will never find on your own.
Also, there used to be a prerecorded audio tour of Grand Central station that I found interesting.
The Met (5th ave on the park) is one of the best museums in the world. Take a doscent(sp?) tour.
Best bars and restaurants in the world, prices to match.
I have walked the battery to midtown, if you have strong legs it is recommended.
Given the short amount of time I don’t think going to the Statue of Liberty is worth it, but do go to the top of one of the skyscrapers.
Absolutely completely touristy but the open top buses are interesting. I have been going to NY since the 60s and still found it worthwhile.
Walking in NY really depends on where.
If it isn’t clear yet NY is one of the great WALKING cities of the world.