Well, if ever I have friends coming up to London I'd take them to most of the obvious tourist hotspots, Buck House, Trafalgar Square, visit a few museums etc & then get drunk!
Here are some suggestions -
Go on the London Eye, hang out on the nearby South Bank where you can visit BFI Southbank, BFI Imax, National Theatre, Hayward Gallery.
Use the riverboat service to travel up the Thames, you can use the Tate to Tate service which goes from Tate Modern to Tate Britain, both worth a visit. You can also travel by river to the Tower of London.
Visit Richmond Park, the largest Royal Park in London & home to a few hundred deer. Richmond itself is nice, sit by the river in the sunshine & sink a few pints!
Take a themed guided tour, Jack The Ripper, Sherlock Holmes etc
Go to a proper east end cockney boozer!
Try some jellied eels or pie 'n' mash.
Have a nose around Spitalfields Market.
Go to a gig/concert/theatre/club.
Go greyhound racing at Wimbledon Stadium.
Wander round Highgate Cemetery, you can take guided tours or just make your own way around. You can see the tomb of Karl Marx, & other famous people, poets, writers etc.