I echo Smaxie –– it's not one publication (and the writer at that publication is irrelevant), but a consensus from the following publications bodes well whether or not the NYT loves it:
Wall Street Journal, New Yorker, NY Post, Washington Post, NY Magazine, LA Times, Chicago Tribune, Entertainment Weekly
(I would leave the trades like THR and Variety out since those are mainly just read by industry folks and Very Online theatre fans)
Of course, genuine buzz and word of mouth is even more necessary to keep a show afloat; reviews just jumpstart that.