Is there any tourist place near around the New York City, where I spend my summer vacations?

You didn't tell us anything about your son so most suggestions are likely to not apply.

Creativity, achievement or activity - anything that creates a lasting good memory.

My summer holidays have almost faded away except a few scattered events, but one Easter holiday I borrowed the school canoe and spent nearly the whole fortnight paddling around on our local river (mostly) alone and without a lifejacket. It was great fun dodging the barges and riding the great wash they made. The first week was hot but cooled for the second week so during the first week I was in the river almost as much as in the canoe.
That was in the mid 1960s before we were as conscious of river pollution as today and so I developed a mysterious red rash (painless) and mother quickly took me to the family doctor who informed her our local river was the worst "sewer" for 200 miles and I should be kept out of the water.

That is one of my best memories...

refer to a travel brochure for this answer

I think you may consult with trip planner who is specially for Catskills, New York. Example:
Trip Planner

I suggest you a place where you stay and enjoy with many recreational activities near around New York, Inn at Lake Joseph.
Check out here: http://www.lakejoseph.com

If you want the adventurous trip with your family so I suggest you one Inn near New York City. They gives 5-star facility in our Inn that is Inn at Lake Joseph. You can also check this link: http://www.lakejoseph.com

I'll recommend you Lake Joseph it's a best place, where you can enjoy wildlife. For any further information about it check this link.
http://www.lakejoseph.com/info.html

I always suggest Key Harbour Lodge to the tourists in Ontario.

Near the bottom of the Whereto>City screen is a button to change states. Select it first, so you can change to New York, then enter Troy when it returns to the City screen.