The thing about NY is you can see shows every night and still have plenty of time to do other stuff. I visited last March. Got in on Tuesday evening, saw a show, saw two shows on Wednesday, a show on Thursday, a show on Friday, two shows on Saturday, and two shows on Sunday, then flew home again Monday afternoon. I still had time to use all five tickets of my CityPass, head all the way downtown to check out the Brooklyn Bridge and the Bodies exhibition, do Top of the Rock, a Lincoln Centre tour, a nice stroll around Central Park, a lot of shopping, a lot of eating, and a lot of wandering around.
It's less easy in London, as we have Tuesday and Thursday matinees over here. But there's still Friday, I suppose...