Rent.
There were a whole slew of people here recommending it. My guess is that it doesn't work for the Finnstep. Hamilton doesn't surprise me as much because it is based on a figure in U.S. History (Though it is an awesome play).
We have Hello Dolly (Hurtado & Khaliavin), The King & I (Bashynska & Beaumont and Lavrova & Gart), A Chorus Line (Yoshida & Nishiyama and the lesser known Russian team from Lombardia), and I do think someone has Cats.
We have no Pirates of Penzance as far as I know or even any Gilbert & Sullivan. I don't remember seeing any South Pacific, Oklahoma, Music Man, or Carousel.
But, by golly, we have about 8 42nd Streets, 7 Singing in the Rains, 6 Cabarets, 4 Bonnie & Clydes, and 4 Too Darn Hots. Also a number of Puttin On the Ritzes and New York, New Yorks.