Do you use the different tabs? If so, if you want to send NYT emails to a different tabs, just pick one up (click and drag) and put it into the tab you want. A message will pop up to say 'Do this will all future messages from xxx' (or something like that) just click yes and they'll all arrive there in future, rather than clutter up your main inbox.

I also use the labels and archive a lot. Gmail is very useful, but you have to put in the work. *g*