I look at the ToC first and scan it for writers I like. I go to their articles first, and generally read them, especially if the subjects are promising. My second choice would be articles with writers I haven't heard of but whose titles are intriguing in some way.
If I tried to read it start to finish, especially the entertainment listings and Talk of the Town, I'd rarely get past, maybe, Shouts & Murmurs. I still read TotT editorials but generally skip over the short features.
If none of the stand-alone features is appealing, I'm most likely to find things I'm interested in in "The Critics" section, especially the "Books" pieces. Not because I want to find good new books, which I generally do in newspapers or other magazines or social media, but because I want to read the articles themselves, which are usually essays on the subject of the book, sometimes but not always including multiple writers on the subject (if I were the authors, my thrill of being featured might be slightly diminished by writers other than myself publishing essays about my subject).