About places to stay, I can't recommend any particular hotels but the area between Hammersmith and Earl's Court is quite nice, close to the venue and there's lots of hotels there (both chain and upscale). Just my opinion though!
The venue is very close to both Shepherd's Bush Station (Central Line) and Shepherd's Bush Market Station (Hammersmith and City Line). The Hammersmith Station is also in walking distance (15-20 mins) and served by the Piccadilly Line, Hammersmith and City Line and District Line. You'll need to take into account that since it's on a Sunday (in the evening, I suppose) you won't be able to use the night tube if the show goes on until late, but Uber is always an option and there are also some night buses that stop nearby (the N207 for example goes into Central London).
Tfl map: