Do not miss Mary Stuart with Janet McTeer. This is great theatre. It will be playing a limited run at the Apollo this fall. This qualifies as a must-see. The only one I can think of.
Joseph Fiennes in Epitaph for George Dillon looks promising, but then I have a distinct case of the severe hots for Mr. Fiennes the Younger so I am prejudiced.
What will be at the National or the Donmar?
The English do Shakespeare better than we do. Also the classics seem to fare better in London. Go see their specialty. We do musicals better.
Many of the musicals currently playing are American in origin or have already played long runs in the US or are about to open or have the decided whiff of "jukebox" about them. Billy Elliot won't be playing any time soon in the US however--2 years probably. Mary Poppins will probably open in NY within 6-12 months.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher