Food, Sights, Entertainment

breakfast club, W1
If you say you are here to see the mayor, they take to a private club downstairs.
Covent Garden Market
walk through covent garden and see some street performances
South Bank
walk to South Bank over the Thames. They usually have food markets on the weekends.
Dominion Theatre
watch a london musical. I would recommend Jersey Boys or We Will Rock You
Dirty Martini
Enjoy a cocktail before calling it a night... or beginning one!