Check the cabaret venues such as 54 Below, Birdland, Joe's Pub ect or event the concert halls. Because most shows are dark on Monday, every event that wants to have people that are currently starring a show will do that event on Monday night and there is almost always something great going on. For example next Monday (as in May 4) is the New York Pops Birthday Gala at Carnegie Hall with an all-star Broadway cast (Laura Benanti, Kelli O'Hara, Sutton Foster just from the top of my head). Of course something as big as that doesn't happen every week, but you never know!
I know this doesn't really answer you question but my recommendation if you're looking for something do see on a Monday night would always be to check those type venues/events first.