Where should I take my cousin in london ?

Hey so my cousin is coming round and she has never been to London before I have I am planning to take her to the new M and M world and westfield shopping and the high street I know their are so many amazing places to see But where should I start I only have to show london in one day. She is very arty girl and I wanted her to take her to museum but I can't remember which one are for free ??? PLEASE HELP WITH ANY IDEAS and of course we should be going to the main ones like london eye and big ben what else ? I only can show her I only have time to show her the key points of a huge city of london !