The Museum of Natural History is one of the best places for kids. But be aware that it is HUGE and might be hard to do all in one day. There are multiple floors, Hayden Planetarium, and special exhibits going on all the time. If you want to do it all, it can be expensive. However if you are content to walk through just the museum - guess what? It's a SUGGESTED DONATION so you can pay whatever you feel is appropriate!!!!
Not much needs to be said about The Bronx Zoo This place is amazing and has hundreds (if not thousands) of outdoor and indoor exhibits. From seals, to bats, to butterflies, there is something for everyone. We recommend getting a membership if you live close enough. 2-3 visits and it's paid for! Plus it includes the Central Park Zoo, The NY Aquarium, Prospect Park Zoo and Queens Zoo. If not, definitely get the Total Experience Tickets - this allows unlimited entry to all of the special exhibits not included in your general ticket price - the bug carousel, the butterfly house, the Congo, the children's zoo, the 4D movie, wild Asia monorail, zoo shuttle. If you pay a la carte for these things, it will cost a lot more. Sometimes if you go in the off season (early spring, late fall, winter) you can get into Congo for free. For the tight budget, go on Wednesdays - it's free (donations are requested) but does not include exhibits mentioned above. However this is the most crowded day of the week! Parking is $15 regardless of ticket price. If you are lucky, you can find street parking.
Times Square is in the heart of midtown Manhattan. A visit to NYC cannot miss this! Technically around the area of Broadway and 42nd street, here you will find all the lights, sights and sounds you would expect in NYC. For kids, check out M&M World on Broadway between 49th & 48th streets (FREE). Even if you buy nothing (which will be tough) it's worth it to see the hundreds of varieties of M&M's you never knew existed! Go on the M&M simulator to find out what M&M personality you are. BUDGET HINT: Buy a pack of M&M's for your kids BEFORE you go in and promise it to them after you leave to avoid the expensive candy inside. Then try Toys R Us on Broadway between 44th and 45th streets (FREE). It has an ice cream shop and indoor carousel for a fee. A giant robotic dinosaur and a life size Barbie house! Definitely catch a show on or off Broadway. If you aren't picky, try the TKTS discount booth for last minute deals. And for an awesome view of the city with virtually no lines and for the cost of a drink, go to The View restaurant in the Marriott Marquis located at Broadway and 46th street. The restaurant is at the top of the hotel, it rotates slowly and offers amazing views of the city all while sitting and relaxing and having a cocktail. Reservations for lunch or dinner are suggested but if you go up before 5 (especially weekdays), you shouldn't have a problem getting a great seat. It costs less than the observation decks at the Empire State Building and Top of the Rock. And you can bring the KIDS! However, if your children are of the loud, high energy brood, I would skip this.
Rockefeller Center is another must see - especially around Christmas time! The tree, the skaters, the holiday windows are sure to put you in a festive mood. We recommend going early, as it gets more and more crowded as the day goes on. You could go to the Top of the Rock for incredible views of the city (FEE). Within Rockefeller center is Lego store. See a Lego rendition of Rockefeller Center and a giant snake! 5th Avenue is world famous for it's shopping. Right around the corner is St. Patrick's Cathedral located at 5th Avenue between 50th & 51st streets. It is stunning. Be aware that it is currently being restored and has scaffolding inside and out. This is scheduled to be there until at least the end of 2014. Nearby is Radio City Music Hall - home to the famous Rockettes. If you can, catch a show! Located on the Avenue of the Americas between 50th & 51st streets. Finally for the little (and big) girls in your group, The American Girl store is located at 5th avenue on 49th street.
If you head south of Midtown, there is more to see! The High Line is a gorgeous elevated walkway that runs along 10th avenue from Gansevoort Street to 30th (FREE). Check out South Street Seaport - it now has an ice skating rink! Take The Circle Line for cruises around Manhattan and the Statue of Liberty (FEE). Of course there is the iconic Empire State Building where you can go up to the observation deck for a fee. And last but not least is the World Trade Center Memorial located at Liberty Street. While you are downtown, check out Chinatown and Little Italy for amazing eats!
So I know we have just scratched the surface and we have left out a TON of other things. But I hope this will help you plan a successful, stress free visit to NYC with your KIDS!