Any advice, info, and help about Connecticut suburbs and New York City?

Hello, my name is Santiago. I have a wife and four kids (boy 17, girl 15, girl 15, and boy 9). I figured you might need to know that for my question. Recently I got a job offer in New York City, currently I live in Florida. Here I make almost $400,000 a year as a CFO, and I got a promotion/transfer to NYC, where I could make up to $850,000 a year! Now, $395,000 a year is a fantastic salary, so unless I enjoy living there as much as here then I don't feel it's absolutely necessary. Firstly, I hate cities (I live in a gorgeous upper-middle class suburban community outside of Ft. Lauderdale, and I'm not sure if I can handle city life) I've never been one for the concrete jungle. So what I figured was I could maybe live in Connecticut or New Jersey in some close-by suburbs. I am not too good with cold weather but that I can handle. Do you know of any nice, pretty suburban towns near new York city for one to live in? Thanks! I just don't feel comfortable with my kids/wife in such a big and dangerous city (I'm sorry, I've had some bad experiences with NYC)