Find out what her favourite shows are, and see if there's a nice book to go with that.
For instance, Hamilton: The Revolution is an awesome making-of. Or something like RENT: Broadway singer's edition, which is great for auditions and the like. Just a script can be cool as a gift as well, like Spring Awakening.
Find out her top three, and let google be yr friend. Or if you really want to make a splash, look on eBay