How exciting! Since I don't know how long your trip will be I am going to assume it is a few weeks. There is so much to do in this country but if you stick with the SW I would suggest going through Santa Fe (It is suppose to be beautiful during the holidays and gives you a feel for Indian culture. Of course the Grand Canyon is a must and then keep going to Houston for NASA especially if your son is interested in space.
And if you do choose to head to NYC the answer is yes ... lots for an 8 yr old to enjoy and NYC is a magical place during the holidays and many museums full of culture and science, but I agree with others ... you really would enjoy the SW experience and temperatures are mild in the south during winter, you should be fine especially if you are looking to rent an RV. Do keep us posted.
Also ... where are you coming from?