As someone who lives nearer to London than NYC (not that near, but I visit both cities as often as my bank balance allows!), I would second the view that you should see something which isn't officially scheduled to transfer (yet).
Priscilla is a huge favourite of mine because it's so much fun - not to mention spectacularly gorgeous to look at, features an award-worthy performance from Tony Sheldon as Bernadette and there's
nothing else quite like it playing anywhere on Broadway (or probably anywhere else in the USA for that matter)!
Sister Act is also worth a look - once it hits its stride it is just a joyous event and Patina Miller is fabulous in the Whoopi Goldberg role.
Obviously it depends on where your tastes lie (camp musicals / straight plays / original productions etc etc) but I hope you get to see something you really love.
And to answer one of your questions: there is a TKTS booth in Leicester Square and it also sells discounted seats up to 7 days in advance. Website:
http://www.officiallondontheatre.co.uk/tkts/
Seen some shows in my time....
Updated On: 7/3/09 at 05:44 PM