I just got my first trip back to NY in a very long time. I'll be there in late July (July 27 thru Aug. 1) Now soliciting advice from strangers on what theatre and performing arts events should be on my must-see list. Company and Into the Woods are 100% confirmed, but everything else is open.
A Strange Loop is a strong likelihood. Were it still playing, Hangmen would have been a definite.
None of the other current musicals on Broadway interest me, so if there are other plays (Off and Off-Off Broadway) OR classical, jazz, dance, cabaret, comedy etc. shows you'd have on your list for that time period, do let me know!