I think my favourite, overall, is The New Yorker. Good blend of culture, current affairs, as well esoteric/niche interest stories. In my uneducated opinion, very well written and edited. I always skip the local goings-on-about-town (as I'm not in NYC), and will often skip the short fiction as well. There are pages with ads, but I've never considered it a nuisance like in some other mags.

I've tried reading a few other publications but find them a chore or a bore to get through.