WOW! You will have a very busy, but definitely a wonderful time in NYC!
It is certainly a destination that must be experienced to be fully understood.
I have traveled up to the city many times just for the day to go shopping, so I know how much walking is required, but I think you may just do some drive-bys on your bus.
I also want to add that I do not think going to a Broadway play in NYC is that critical anymore, since so many plays now travel all the country. Traveling to see landmarks specific to the city is much more special--there is nothing like the Statue of Liberty up close.
I do recommend Radio City Music Hall at the holidays, and I agree with everybody else how special the city is with all the decorations, but it also becomes extemely busy and quite expensive, and the wind whipping through the skyscrapers can make for a chilly experience.
Enjoy your tour, and make sure to get some selfies in Times Square, etc.