Here is some information to assist you in planning your time in London:
West End shows: http://www.visitlondon.com/things-to-do/whats-on/theatre/top-ten-musicals#wEyce31jPh3sSJMz.97
The Lion King, Phantom of the Opera, Wicked, Thriller, Mama Mia, Book of Mormon, Les Miserables, Kinky Boots, Jersey Boys. And many, many more…
Other things to do in London:
Afternoon Tea – Aqua Shard http://www.afternoontea.co.uk/uk/london/south-bank/aqua-shard/
Afternoon Tea (with/without Champagne) – Grosvenor House Hotel http://www.parkroom.co.uk/menus/afternoon-tea/
Open-top bus tour around London https://www.theoriginaltour.com/
The London Eye - https://www.londoneye.com/
St Paul’s Cathedral - https://www.stpauls.co.uk/tickets
Tower of London - http://www.hrp.org.uk/tower-of-london/visit-us/tickets-and-prices/#gs.As=2KBg
Buckingham Palace (State rooms open 22 July 2017) - https://www.royalcollection.org.uk/visit/the-state-rooms-buckingham-palace
And here is a link to the London tube (subway) map:
https://tfl.gov.uk/maps/track/tube