First NYC is safe, contrary to what Doris Day says. A great place for lunch or dinner with kids is Mars 2112. Think it is 49th street and Broadway or 7th. Can't remember. It is a replica of Mars with aliens roaming around talking to the kids. Ellen's Stardust Diner is great too. Google it. 51 st and 6th I think. Is going and dancing waiters and waitresses. Always a hit with kids.
For parking: go on line and search parking garages in NYC. You can get some great deals. You will need to print out the coupon or page. Stick with Icon parking garages.
Staten Island Feery is great and you can see the Statue of Liberty and it is free. South Street Seaport if great. There are several old ships there.
Central Park Zoo is ok. A carriage ride around the park is nice. Museums: sin e you come from Chicago, I would not recommend them. You have plenty in Chicago.
Best pizza I town: Johns Pizzeria. 260 West 44th street. It is an old church with beautiful stain glass done and murals.
If you want to see a show. The Gazillion Bubble Show is a blast. Your kids are the peccect age. Took all my grand kids. You might be able to get discount t tickets on line.
Then there is always Times Square. The biggest Toys R Us with a Ferris wheel inside. Yes you can ride it.
If I think of anything g else, I will write back. Hopefully this will help. The subway is the quickest way to get around town.
Oh forgot about The Intrepid. 12th Avenueand around 42nd Street.
I, I think Rock Hill, Connecticut ere is a Dinosaur Park which is a lot of fun.
Enjoy. nYC is a great city.