Check out the theatre site Londontheatre.co.uk all that is playing off West End and on West End will be listed during your stay. They also post closing and opening dates. I wanted to see Jonathan Bailey in Richard II at The Bridge Theatre and Cate Blanchett in The Seagull at The Barbacan so booked to secure decent medium prices seats early. Also read theatreboard.co.uk it's similar to allthatchat.com