Standing at the Sky's Edge is a must. IMO.
The additional things that are on my list for July 4 are Hello Dolly, Boys from the Blackstuff, Starlight Express, Mnemonic at the National, Passing Strange at the Young Vic, Spirited Away, People Places and Things and Slave Play. (I'm curious to see that with a non-US audience.)
MarilynMonroeSmash said: "I’d love to get some recommendations for my London Trip around July 4th. I have my list, but I’m sure I may be missing something! The shows on my radar are: Bluets, Slave Play, Mean Girls, Kiss Me Kate, Opening Night, Standing At the Sky’s Edge, Two Strangers, The Constituent, Next to Normal, Hadestown, and The Devil Wears Prada.
Any other recommendations?"