This is actually interesting, because your list includes a lot of things that were invented/developed in New York.
The New York arts:
* If you're looking for the Broadway experience, you won't find it anywhere but Broadway (West End sometimes tries). If you want to define theater a little more broadly, though, there are a lot of options. West End is a different beast, but I think it's actually a bigger scene. For other kinds of theater, Tokyo is also fantastic, and I hear that Melbourne, Australia has a huge theater scene. If you define theater more broadly to include film, LA beats out New York by a mile.
* New York is the jazz capital of the world right now, but New Orleans, Memphis, and Chicago have traded that role and all have a huge scene. That said, jazz basically grew up in Harlem, so it's hard to beat New York.
The non-New-York arts:
* Boston and SF probably have the best classical music scenes in the US. Outside of the US, Vienna holds the title hands down. Like in most arts, New York has the big spectacle (the Met Opera and Carnegie Hall), but in classical music it has a lot less less depth.
* In terms of old artworks, New York has the biggest collection of old works in the US, but Paris, Barcelona, London, and Rome are all huge and probably more notable. In terms of new art, LA is the place to be (in the US).
Again, I said that New York is good at all of these things, but it's not exactly head and shoulders above the rest of the world unless you specifically want a New York experience. It sounds like yours is Broadway, and that's fine, but it's not a universal desire.
I personally prefer to travel to New York when I want to see something on Broadway or at the Met Opera, and that's (IMO) a lot better than living there 24/7.