@Diest TKO,
It's nice to visit the Tate Modern- nice cafe, good food- by the side of the river, and walk across the wobbly bridge to St Paul's Catherdral area. Last time I was there, I went to Monument (it's a tube station, near Bank (the Bank of England- which has a free money museum btw) and climbed to the top of the actual monument which is a tower commemorating the Great Fire of London 1666. The views from the top are rewarding.
If you walk down Ludgate Hill from St Paul's you can walk up Fleet Street, and go into Ye Olde Cheshire Cheese, a pub dating from before the fire.
From there you can reach Covent Garden on foot, maybe going through Lincoln's Inn Fields which is interesting, not fields but the traditional haunts of lawyers, barristers, the robbing classes.
London is awfully big.
Enjoy!