HI! I moved to NYC about 1 1/2 years ago from Los Angeles with my son who was then 3 years old and my daughter who was 6 months old. They are now 5 and 2 years old, respectively. I don't know too much about Queens or CT, but I know Brooklyn (Park Slope, Cobble Hill) is a lot like NYC. My husband works near Grand Central and we live on the Upper East Side. I absolutely love NYC!! It's really easy getting around with the kids via bus or taxi. I don't ride the subways much with my daughter. The subway stops where we live do not either have elevators or ones that work.
The biggest adjustment to the City was living in an apartment, especially with a baby and no washer/dryer in the apt. Usually when we were going through a transitional period with my daughter like sleeping through the night or taking the bottle (as opposed to the breast) we explained to our neighbors and they were very understanding that it would take a couple of days. We also gave them a bottle of wine.
Our building has a washer/dryer so I just do really big loads or I send our laundry out( costs around 70 Cents per pound). And everyplace delivers from the grocery store, dry cleaners to the restaurants. I really like FreshDirect to order our groceries. They are in Long Island and you place your order over the internet and you pay around $6 for delivery. They are very popular.
We also have a car in the City but we park it about 50 blocks from where we live because it's really expensive to park in our building. We actually don't use our car much because it's easier to use mass transit if you're in the City. We use our car if we want to visit Brooklyn, upstate NY, or NJ.
There are parks where we live with a lot of kids, especially if the weather is really nice. My son always sees one of his friends or finds another kid to play with. During the winter, it's a lot harder. You're indoors a lot because it's too cold and the winters are long from Dec. through March sometimes April. I go to an indoor playground and its really crowded but there's not much you can do. My building has a children's playground and I sign my son for a class to take during the winter. I've met other moms and a lot of nannies at the playground or at classes and in my building. When we first moved to NYC we were fortunate to find an apartment with a big yard. We had playground equipment for both of my kids. We lived there a year and then moved to another apartment because our landlord decided she wanted to return to the city. The apartment we currently live in does not have a yard and my kids don't miss it. They always want to go to the park where there are other kids , sandbox, and swings.
We're problably be here for 1 1/2 years and we considered about living elsewhere because of the rent. But for me, it's easier to get around and take the kids to the museums, parks, zoo, and restaurants. My husband works late and travels a lot so for me its a lot more convenient to live in the city. And the shopping is great!
Good Luck and I hope I was able to answer some of your questions.