Have you tried The New York Review of Books (nybooks.com)?
As venerable a cultural and literary institution as TNY, but the signal-to-noise ratio is much higher; less fetishization of the NY cultural scene (NYRB, despite its name, doesn't cover NY, and is ironically seldom about book reviews), less glitz. The paper edition is wonderfully old school, basically a tabloid newspaper format with zero thought to design or typography.
From what I can tell, all of their content ends up on the site. Their Kindle edition has both the digital version and the paper layout in the same file so you can switch between the two modes.