I woule heartily recomend seeing a Shakespeare play at the Globe Theater. A raucus time and you will get a kick out of the standing room stage area. We saw Macbeth and it was a fantastic experience. Next to the Globe is the Tate modern which is worth visitng depending on your taste in art. We lucked out and it was free to enter that day. It only took us a half hour to find the works of art we were interested in. Next to the Tate is a nice eatery with a great view of the Thames where I had a great White beer which was smoother than silk. Oh, next the the Globe Theater is an ice cream truck with the 99p cones.
The Tower of London is at one end next to the Tower Bridge while the London Eye is at the other end near Big Ben. We found taking the river boats a great way to get around that day.
Our trip to Westminster Abbey began after the changing of the guard. We did this on a Friday and eventually walked to Picadilly Circus via Trafalger Sq. On Friday night the National Art gallery is open till 9 PM and full of incredible collections of artwork. Later, we strolled to Picadilly Circus and ate near there in the Covent Garden area. Full of life and energy till the wee hours.
St Paul's Cathedral is a place where you may find yourself spending more time then you planned. The climb up the spiral staircases to each level is bettter than a stair master and the views are well worth it. The dome is so inviting that you will find yourself in a contemplative or spiritual mood when you sit under it and take the whole cathedral in. Once you leave the St Paul's, you can walk across the Millenium Bridge or head in another direction to the Tower of London.
The British Library is near the Britsh Museum and well worth visiting. The museum needs time, the library is short.Seeing original works from around the globe makes these books come alive in history. The room devoted to the Magna Carta is very informative and you will leave the library understanding the power of print.