Simply in strolling the River, you can see much of what London has to offer. A stroll from the Tower Bridge, along the South Bank, to Lambeth can show you a wealth of sites. You can see the Houses of Parliament, not to mention the Archbishop of Canterbury’s home, Lambeth Palace, and even the famed Globe Theatre, which in its time has seen the best of Shakespeare. The Tate Galleries are along this walk as well, along with St. Paul’s Cathedral, plus South Bank Centre, the London Eye, and The Temple. Boat rides are also available, taking you to the Thames Barrier, the Dome, or Greenwich.
Naturally, a trip to London would not be complete without a visit to Westminster Abbey, the place where kings are crowned and bards are buried.
The Houses of Parliament are must sees as well — especially if ytou can get a seat in the famed Strangers Gallery, especially during Question Time. There are a number of surprisingly entertaining things to do here. A must if you enjoy government and/or debates. On that note, check out the Inns of Court as well.