Taxis can seat four passengers. Unfortunately, babies are counted as people so if you're three kids and two adults traveling you're out of luck unless you can convince the taxi driver to seat you (some do). If he does, leave a better than 20% tip! Taxis do not carry infant or booster seats and children are allowed to ride without one. Most New Yorkers don't bother with a booster seat though some will carry an infant seat for the baby.If you want your child to be strapped into one, bring your own. The trunk in a taxi is huge and a Maclaren stroller will fit inside without having to be folded up.
Subway can be fun as well as a challenge. While older kids will love the clatter of trains and enjoy watching the express rush by without stopping, parents with younger kids may have to negotiate an ancient system with their strollers. There are few escalators or elevators in New York subway stations and the odds are you'll have to lug your stroller up and down the steps. Fortunately, the tracks are just a few feet below street level so the lugging is not extensive. If you are alone and stand around long enough, someone will offer to help. If you have a stroller and want to take it onto the train without folding it, you must use a subway entrance with a manned token booth. A doorway next to token booths (labeled 'Emergency Exit') provides entry for passengers in wheelchairs or people with strollers. Inform the token booth attendant that you wish to use the door, slide your card through the turnstile and turn it with your hand, return to the door and pass through. Looks complicated but it is really quite easy! Technically, children under 48 inches ride free on the subway.
Bus. If you have younger kids, note that strollers must be folded and carried onto a bus.
Walking is the best way to enjoy the city. In winter it can get very cold and you will spend more time outdoors than you do at home so dress your children in warm clothes. Layering is the best way to deal with the contrasts between the freeze outside and the warmth indoors. If you have young children, bring your stroller.
See and Do
(See the New York City pages for general details on the items below. The information here is kid specific!)
Central Park: Heckscher Playground (Ages 1 to 7) is the oldest playground in the park. Recently restored and reopened, the playground has large sandboxes, numerous sprinklers, watery canals, and a huge climbable rock that is a magnet for kids.
Central Park: Ice Skating (Ages 4 and up) at the Wollman and Lasker Rinks is a fun winter activity, set as it is in a Park with leafless trees and the possibility of snow all around. Wollman Rink is best accessed from 60th street on the East Side, while Lasker Rink is in the northern end of the park (best to enter on 7th Avenue and 110th street).
Central Park: Zoo (All Ages)  with penguins, puffins, polar bears, and sea-lions is fun for children of all ages. The feeding of the sea-lions (daily 11:30, 2, and 4pm) has become an attraction by itself. Nearby, the newer Children's Zoo (Ages 2 to 8) is more interactive where kids can feed goats and llamas or just sit in a mock turtle egg. The two zoos have separate entrances but a common entry fee. The cafe in the zoo has kid friendly healthy food.
Children's Museum of Manhattan (upto 8 years) has imaginative interactive exhibitions (most recently on the Greeks) that should entertain and educate the kids. Across the street, Cafe Lalo has excellent kid sized hot chocolate for cold days.
Macy's Thanksgiving Day Parade (Ages 4 and up) wends its way down from 72nd Street to Times Square along Central Park West and Broadway. Marching Bands and the balloons of every popular character from kid TV make this a popular event for children. The parade is long so you might want to keep the younger kids at home, especially if the weather is cold and wet. Alternatively, take the kids the previous evening for the blowing up of the balloons on 77th Street south of the Museum of Natural History.
The Metropolitan Museum of Art is the premier art museum in the Americas and one of the largest of its kind in the world. The Met has programs designed especially for children  that are a great way to introduce your children to art. Many are free with admission and most don't require reservations. Start with Art with the Met (Ages 3 to 7) is a short, curator guided, walk through parts of the museum with the children sketching and building stories about the artwork they see. No reservations are necessary so you can just show up for this (check the website for days and times). Hello Met (Ages 5 to 12), for older kids, is more discussion and presentation oriented. In Spring and Fall, there are drop off programs for older kids (check the website for programs and times) that usually require reservations. Reserve one, drop your child off, and enjoy a child-free hour at the Met!
The Museum of Modern Art (MOMA) MOMA offers a variety of programs for children  ranging from guided tours to storytelling and sketching. An audio guide designed for children is available (free with admission) and a free family activity guide is a useful way of explaining the art to young children. Most programs require reservations, so check the schedule and make reservations before you go!
PS 1/MOMA With sand and water all over the place this is perfect for both kids and adults on a summer weekend. The exhibits are odd enough to enchant everyone and the galleries, especially in the basement, weird enough to keep the kids happy. Beer is available outside so parents can relax while the kids dig into the sand. PS 1 is in Long Island City, Queens. Take the 7 train from Times Square or Grand Central. Bonus: Take the water taxi (from the Water Taxi Beach) to get back to Manhattan.
(Please include only those hotels that you think a family with kids may have a special reason to stay at (a playroom, babysitting services, listening services, special rate for kids, etc.)