The New Yorker and NYRB have already been mentioned; they'd be my top two.
In terms of less mainstream sources, for thought-provoking long-form pieces mostly arising out of an economic justice perspective, I'd suggest Current Affairs.
Oh, and if you're interested in literature, which more broadly extends to culture throughout the decades, then the Paris Review has an incredible tradition of long-form interviews.
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The New Yorker and NYRB have already been mentioned; they'd be my top two.
In terms of less mainstream sources, for thought-provoking long-form pieces mostly arising out of an economic justice perspective, I'd suggest Current Affairs.
https://www.currentaffairs.org
And though it isn't a periodical, for long, smart pieces on sociology, history, economics, contemporary society, etc., I'd suggest Slate Star Codex.
i.e. http://slatestarcodex.com/2014/07/30/meditations-on-moloch
Oh, and if you're interested in literature, which more broadly extends to culture throughout the decades, then the Paris Review has an incredible tradition of long-form interviews.
https://www.theparisreview.org