It certainly is vibrant; at least, the areas I saw were. Lots of people, lots of small businesses, and lots of activity. I know of nothing like it in Detroit. I'm not saying there aren't parts of the city where similar traits exist. Even if there are though, they don't exist to the degree they do in New York.
Yankee Stadium is lovely. It is one great baseball park. I still prefer the classic stadiums such as Fenway in Boston (nothing personal, Yankees fans, and I'm not trying to trip your triggers either) but the new Yankees park is well built. You're reasonably close to the field wherever you are, and the sight lines are fantastic. After seeing it and PNC Park in Pittsburgh, you really understand that Detroit messed up badly with Comerica. I don't quite get why they played 'New York, New York' after a Yankees loss though.
St. Patrick's Cathedral is a gem. I'm glad we went there for Mass.
Times Square was pretty crowded. It was a summer Saturday evening when we walked through it though. I can't imagine what it must be like on December 31st. I don't think I want to know either.
The Oculus is awful; four billion dollars for what amounts to a shopping mall. It looks like a massive skeleton which has been bleached white by desert heat. I read that it's supposed to be a dove extending its wings. A hideously oversized, very dead dove maybe. Plus it's entirely incongruent to downtown Manhattan, where it's part of the World Trade Center. I don't see it as anything more than a monument to hubris quite frankly.
The prices weren't all that bad. Other than the shops which were clearly aimed at the more affluent, and you find those everywhere, I thought that the grocery, restaurant, and cost on general amenities comparable to what I find in Michigan and its surrounds. I do gather that housing and parking can get expensive. Fortunately, that did not affect me.
I don't know if I could live there. There are just too many people, the metropolitan area is so spread out, and the sensory overload of the town can be staggering. But I definitely like New York City. I look forward to my next visit.