Let's start with this: be hyper-local. I should be able to easily plan a trip and tour to New York without ever leaving the NYT website. I should be able to know every single Broadway and off-Broadway play that will be running when I get there and be able to get tickets NOW.
Reporting: How about being actively antagonistic toward government? How about real, hard-hitting government coverage? How about tracing every single dollar, favor, and deal until the politicians don't just hate you, but actively FEAR you.
Editorial: how about some informed opinion pieces? How about starting to peel apart complex topics in multiple parts and report TRUTH rather than both sides?
Gee, you know, that sounds like a ... newspaper. Shame this country doesn't actually have one anymore.
Sure, the NYT gets their lunch stolen, but mostly by one offs.
An aggregate of clever obits. A repackaging of Nelson Mandela's death. Could you predict those IN ADVANCE? Doubtful. Chasing them is like saying "We need to create Gangnam Style". Great. But it isn't going to happen.