Hot Mess - The Other Palace (Cast recording is available to stream, give it a go!)
Death Note: The Musical - Barbican (World premiere and a no brainer if you like the source material)
And if you're day-tripping Leicester Curve will have the world premiere of The Silence of the Lambs Musical. It should be possible to do a two-show day with Birmingham, if you wanted; I did it over the Christmas period with Sherlock Christmas/Sound of Music in Birmingham and Leicester, respectively.
The Comedy About Spies starts August 1. There may still be a sale fir front row tix. I dont know if you would miss some action from there. But we saw it last year and it was hysterical (if you like this kind of humor - bad puns, wordplay and slapstick galore)