South Pacific is about as great a production as we're ever likely to see of South Pacific. It can't quite mask what I think is a bizarre element of the writing - Act Two peaks with "This Nearly Was Mine"... and then there's 20 minutes of book still to go, with all of the action offstage. But it's so well directed, designed and performed and configured so specifically for the Beaumont stage, it probably would not have the same impact anywhere else.
Not sure how and if In the Heights would fly in London. I think the London critics would eat the show alive for its soap opera-ish plot and sentimentality, but the score has charm, with some fun, quirky lyrics and I liked a lot of the choreography and staging.
I'd bet that Hair will make its way over.
As far as new things to see, the fall season includes: Tracy Letts' new play, Superior Donuts; Hugh Jackman and Daniel Craig in A Steady Rain; revivals of Neil Simon's Brighton Beach Memoirs and Broadway Bound, directed by the wonderful David Cromer; revivals of Bye Bye Birdie, Ragtime and Finian's Rainbow; the new musicals Memphis and Fela!; Sarah Ruhl's new play In the Next Room; a new Mamet with Race and an old Mamet with Oleanna; Sienna Miller in Patrick Marber's After Miss Julie; the Donmar's Hamlet with Jude Law; a revival of The Royal Family; and Carrie Fisher in her one-woman show, Wishful Drinking.
Since you seem to be inquiring about the musicals, you might want to investigate Fela! and Ragtime and see if they are for you.
Begin at the beginning and go on till you come to the end: then stop.