A week is a long time and you can see a bunch. Some really great suggestions so far..and don't be afraid to act like a tourist, trust me, no one in NYC cares.
A few things: You mentioned family so if you are bringing kids, what do they want to do?
The Staten Island Ferry was a big hit when my kid were young: NYC from the water is neat. Any of the numerous ferries are enjoyable.
Comedy Clubs. I haven't lived in a city since San Diego in the 80's and I always enjoyed seeing comedians live. If you have a favorite that is playing that could be fun.
I know this suggestion may not fly, but (and I have mentioned this in other threads) bus tours/walking tours are great for first timers in any city. I have done them all over the world and they has made the following days stay much more enjoyable and informed. Absent locals on your squad, it is the cheapest, best way to get acclimated with a family in tow.
https://www.tripadvisor.com/Attractions-g60763-Activities-c42-t174-New_York_City_New_York.html
A friend of mine who is an amateur chef likes to go to one day cooking schools. He has done them all over the world and loves them. He did one in NYC and said it was great.
https://www.yelp.com/search?find_desc=one+day+cooking+class&find_loc=New+York%2C+NY