Central Park with small zoo and playrounds. Museums of Natural History ( all kids love it). A ride on the free Staten Island ferry - beiw fo the harbor, Lady Liberty and great veiws of the city on the way back.

With a small child I would stay on the upper west side, which is a family area with a lot of restaurants where small children are welcome - esp if you eat outside of peak hours (avoid lunch/brunch at 1 pm and after or dinner at 8 pm).

For hotels looks at the Beacon - which has suites if you contct them directly - the Excelsior, Lucerne and On the Ave.

My 4 year old grandson loves the subway! And the dinosaurs at the Museum of Natural History. Make sure you do both.!

When on the subway, be sure to go the first car and look out of the window of the door at the front. You can watch the tracks and lights zoom by. Fun for adults also.

All these suggestions are great. When my kids were little, they loved taking a bus down 5th Avenue (but it can be slow due to traffic).

The bus is interesting as well, and we take them whenever possible. I think the slowest buses are the crosstown buses.

If you go Lombardi's pizza, which is one the best any way, and they are not busy, they will show kids the coal burning ovens.

Some of the best ice cream are the Chinatown Ice Cream Factory and Cones on Bleecker.

There ars some inexpensive but fin candy stores especially Economy Candy and the handmade stuff at Evelyn's.

If he knows Alice in Wonderland, he will love the statue in Central Park.

There's a Children's Museum near the Mus. of Natural History that's good for young kids. http://www.cmom.org/
gocitykids.com might have date specific listings.
Newvictory.org may have a performance he'd like.