Westminster Abbey, located behind the Houses of Parliament, is a stunning sight. Founded prior to the Norman Conquest, the white limestone building that you see today was begun in the 13th century. The nave and Henry VII's chapel are in the perpendicular style--England's version of late Gothic architecture--and was largely complete by the reign of Henry VIII.
Once inside the building, you realize why they called English Gothic "perpendicular"--the ceiling soars above you in great vaults held aloft by giant stone pillars. Almost as striking are the crystal chandeliers which line the nave and light the building.
The gilded painting standing to the right of the Abbey's main entrance is a portrait of Richard II--Chaucer's patron and the main character in Shakespeare's historical play of the same name. He is seated on the coronation throne (somewhat oddly, since he was crowned at age 10, and he sure doesn't look 10 in the picture). You can see the throne itself as you continue through the Abbey.
The focal point of the Abbey is the shrine of St. Edward the Confessor, located where the transept meets the nave.
It's made of various types of exotic stone like purple porphyry, but isn't particularly splendid now, since it was demolished when Henry VIII broke with Rome, and inexpertly reconstructed.
More striking (but usually covered so that it's protected) is the original medieval floor that the shrine stands on. The floor is displayed on occasion, so you may be lucky enough to see it when you're there.
Everybody visits Poet's Corner, found near the shrine in the right arm of the transept. It contains monuments to famous authors like Chaucer and Shakespeare. Some of the authors commemorated are actually buried here--like Chaucer, whose tomb is the nucleus of Poet's Corner. One--Shakespeare's contemporary Ben Jonson--has a monument in the corner, but is actually buried to the left of the main doors. See if you can find his real headstone, set into the wall at floor level.
Before you strike off to hunt for Ben, though, check out the 13th century murals on the transept wall. The color is striking, and helps you imagine what the medieval abbey (which would have been entirely covered with such murals) must have been like.
If you'll be in London for several days, be sure to go to the Abbey's Evensong.
Evensong is an Anglican service where the worshippers reflect upon the past day. It can be either sung or spoken. Try to go to a sung service, with the music provided by the men and boys of Westminster's choir. It's a peaceful way to stop and take stock after a busy day.
Admission to the Abbey is $9 for adults, $4.50 for students. Full price admission is expensive, but the proceeds go toward the cost of maintaining the Abbey.
As Evensong is a church service, it's free.
The Abbey is easy to get to; take the tube to the Westminster stop.