I went years ago pre-kids.
We paid for a crappy breakfast of stale rolls and croissants in the hotel but the discovered a great deli next door where breakfast means piles of pancakes, waffles, full cooked or what ever you want, refill coffes etc. There are great delis/ cafes all over. You can eat as expensive or as cheap as you want, we saved the money for sightseeing.
I suppose the must sees are the things you have always wanted to do, I really wanted to skate in NY so I did. We did a bit of shopping but I prefered sightseeing I can visit department stores anytime.
We got the ferry accross to the Statue of liberty but didn't waste time queuing and climbing it as it was foggy, I enjoyed Elis Island but that may not appeal to everyone.
If you are feeling flush I would recommend a helicopter tour if its a clear day or night. We were there for 5 days so we managed a boat tour around the whole of Manhattan but I wouldn't do this if I only had a few days.
Carefull where you stray, there are some dodgy streets just off the main ones, just turn around and head back, unless you are looking for strip joints that is . I actually felt really safe and unless you walk around with a camera glued to your face it is easy to blend in as the people are so diverse.