Don't know about shows, check the listings as the above advice in Time Out online. I suspect you'll already be going to the only thing worth being at anyway. Shoreditch for bars and hipsters (a stone's throw from Hackney where the show is) Chinatown for food (in the West End you can't miss it) Victoria & Albert Museum for arts & culture, avoid the Natural History Museum (full of screaming kids) and the British Museum (full of moody students with backpacks) Take a boat trip from Waterloo pier to Greenwich on a Sunday morning and take in the markets the Naval Museum and the observatory.
Avoid the usual tourist bullshit.