It's a pretty amazing city if you don't have to go and visit on the cheap. If you're trying to do everything inexpensively, you're not going to see the great parts of New York. If you have some money to spend, it's a bloody wonderland of possibilities. Amazing place, and I much prefer it to any European city I've been in.
That said, now that I'm living so near to Chicago, I've taken the time to get to know that city as well. It is also amazing - something for everyone. World class museums of all sorts, professional and amateur sports up the wazoo, amazing music scene for everything from Classical to Indie Rock, shopping for anything you could want, great public transit, and on and on the list goes.