...obviously a non-exhaustive list.
Theatres
The National Theatre (on the South Bank)
http://www.nationaltheatre.org.uk
The Globe Theatre, Bankside, SE1 (close to Tate Modern)
http://www.shakespearesglobe.com
Royal Court Theatre (Sloane Square)
http://www.royalcourttheatre.com/whats-on/
Music
The Royal Albert Hall, Kensington
http://www.royalalberthall.com
The Coliseum (home of the English National Opera), Trafalgar Square
https://www.eno.org
The Royal Opera House, Covent Garden
http://www.roh.org.uk
Galleries
The National Gallery, Trafalgar Square
http://www.nationalgallery.org.uk
The Tate Gallery (Tate Britain), Millbank, SW1
http://www.tate.org.uk/visit/tate-britain
The Tate Gallery (Tate Modern), Bankside, SE1
http://www.tate.org.uk/visit/tate-modern
Museums
Natural History Museum, Kensington
http://www.nhm.ac.uk
The Science Museum, Kensington
http://www.sciencemuseum.org.uk
The Victoria And Albert Museum, Kensington
http://www.vam.ac.uk
Good Listings Sites for what's on in London
Time Out
http://www.timeout.com/london
Visit London
http://www.visitlondon.com/things-to-do/whats-on
