Well, the founder of Lapham's, Lewis Lapham, was previously the editor for Harper's, so that's something else you might want to check out.
However, I feel that Lapham's is unique in that it picks a single topic for an issue, and then goes into great depth on that topic by interleaving primary sources and analysis.
Lapham's Quarterly is unique, and a pleasure to read and hold, but, to be fair, I wouldn't really call it a magazine. But Lewis Lapham has certainly made Harper's into the most interesting, subversive, funny and whimsical high-brow general interest magazine in circulation. The last few issues, though, have taken a slight dip in quality, so I'm following it with some concern.
Like the New Yorker and Vanity Fair, and unlike the Atlantic or the NYT Magazine, Harper's prefers on-the-ground reporting over covering "issues" or "trends". But the writing quality in Harper's tends to be much superior to that of both the New Yorker and Vanity Fair. Harper's best features are usually non-mainstream, and even intentionally bizarre stories.
To get a taste of Harper's, take a look at their regular science column, which I find hilarious. Here's the last one: http://harpers.org/archive/2012/10/0084112.
I post it to HN every month but it never gets more than a few votes...
The Baffler is great, but has mostly cultural analysis pieces and almost no original reporting. I think N+1 resembles pretentious college publications, and frankly I find it quite boring, though I may give it another look.
