NYC born and raised and raised my family here. NYC wonderful place to visit but can be overwhelming, exhausting and expensive. That said, a little planning will go a long way. I suggest you divide your visit to a midtown portion and a downtown portion.
Midtown:
Rockefeller Center Tree is a must.
Agree avoid Times Square - there is really nothing there.
Perhaps walk up through Central Park to Metropolitan Museum or Museum Natural History. For both Pay-what-you-wish admission is available only at ticket counters, where the amount you pay is up to you. Each is fantastic, Natural History may be more appealing to a young boy.
Subway service to Downtown easy. #2 or 3 train on West Side (natural History Museum) or #4 or #5 train if on East Side (Met).
Downtown visit Battery Park for view of Statue of Liberty, go to WTC Memorial. There are self guided walking tours of this historic district.
Food - - - everything you can imagine at multiple price points. Katz's Deli on Houston Street is iconic and a true New Yawk experience.
Feel free to PM me if any questions.