Why not switch to a .nyt TLD? Or .times?
Deviate from .com .net .ca .org and most people become clueless. Especially when users are sending an email, try explaining name@newyork.times is simply the address when a user insists there's a typo and it's missing .com or equivalent. Unfortunately adding a www. before, say on a business card, to denote it's a web address is counter-intuitive in most cases as that just lengthens the domain when typically the reason why one would get/migrate to a new TLD is to shorten it/make it easy to remember.
(as an aside, there is a The Times newspaper in the UK and I'm sure many other places. I suspect ownership of .times would become a lot more bother than it was worth, very quickly)
us.ny.ny.times
In other words, the entire domain name system should read left to right as top of hierarchy to bottom of hierarchy.