N.O.
Ellis Island and the Statue of Liberty can be done on the same day and the kids will like the ferry ride.
The Empire State Building is beautiful at night.
The American Museum of Natural History is fun and more child friendly than the art museums.
The HUGE FAO Schwartz store will be a big hit with your 5 year old and adults have fun too.
Central Park is fabulous to let the kids play outside plus there is a lot of people watching. There is also a zoo there.
There is the New York Aquarium, the New York City Fire Museum, The children's Museum of Manhattan and a huge Toys 'R' Us too.
For the kids...stop frequently, plan a lot of snacks and bring strollers. Make sure your 5 year old has good shoes for walking and I would bring a Baby Bjorn for the 2 month old to give carrying options. Neither of my kids needed a lot of "entertaining" at the age of 2 months, they just need to be comfortable, able to sleep, and able to eat when they need to.
HAVE FUN!!!!! I wish I was going:)