Torch Song, and M. Butterfly comes to mind amongst limited run/new shows - both are revivals of acclaimed plays. Torch Song, IMO, is a show every gay person should see. It's just beautiful beautiful writing. And if either you or your partner are 30 years or below, you get $30.00 tickets (normally priced @ $89.00-$119.00 depending on the night) which is a steal. M. Butterfly begins previews 7th Oct so worth checking out - if you get tickets to first preview, there's added excitement of seeing a hotly anticipated revival before anyone else. I love the energy of the room during first preview.
Out of long running shows, Kinky Boots is a hilarious one with a pretty good score and their original Tony winning/nominated male leads are back in the show right now so it will be a good one to catch. Other show worth considering is Miss Saigon - it's a hot topic of debate on these boards whether that show has any merit or not because of its frankly problematic themes, but I think the story is moving, some of the songs are really good, and it has some of the best performers on Broadway right now.
When Pigs Fly starts previews after you've left (11th Oct. per their website but I think I saw a delay article somewhere, not sure what's the actual date) so that you can pass on. Same with The Band's Visit.
Caption: Every so often there was a rare moment of perfect balance when I soared above him.