Many people who cross London Bridge today wonder why the bridge to the east looks like the London Bridge they imagined. The fact is, London Bridge has fallen down - many times. Timber bridges pulled down by Vikings. A medieval bridge stuffed with houses that crumbled because of a queen's financial mismanagement. A nineteenth century behemoth that was very shrewdly sold in pieces to an American eager for tourist dollars. This is the story of all those bridges, and the bridge that stands in their place today, unlikely to fall for a long time because it prioritizes being a bridge over being an iconic bridge.
Most people who arrive at London Bridge are either there to cross it (because they've got stuff to do), or to do this:
That is Tower Bridge, the bridge many confuse with London Bridge (which Tower Bridge, sometimes calling itself London Tower Bridge, is more than happy to along with, the sneaky bastard).
London Bridge doesn't get quite as many pictures taken of it. It does its job well - its wide and uncluttered, which is a nice feature in a major bridge. If it weren't for its magical name, its unlikely anyone would give it a second thought.
Its most striking feature is the spike that protrudes from the Shard-side of its southern entrance. Unadorned by any plaque, it marks the spot where the heads to traitors like William Wallace and Jack Cade would have sat above the Southern Gate starting in 1577.
Directly to the west of this spike is a building called Colechurch House. Peter de Colechurch doesn't have a Wikipedia page, the poor guy, but at least he has this building (unless it happens to be named after St. Mary Colechurch, but considering its proximity to the bridge Peter made famous, that's doubtful).
Face away from Colechurch House, and you're facing the beautiful Southwark Cathedral, formerly St. Mary Overy. This is the spot where Mary, daughter of the miserly ferryman John, founded her convent using his riches. You can see a plaque dedicated to Mary in front of the Golden Hinde dock, immediately to the northeast of the cathedral.
Speaking of grand churches, cross London Bridge going north, and head a bit east. Here, in the shadow of Christopher Wren's Monument to the Great Fire, you'll find one of the many (many, many) churches he rebuilt in that fire's wake - St. Magnus the Martyr. The steeple has an arched walkway - close your eyes and imagine walking under it and onto the modified London Bridge of the eighteenth century. Be sure to head inside and check out the model of medieval London Bridge in all its glory.
You may as well visit Wren's masterpiece, the reconstructed St. Paul's while you're in this neck of the woods. While you're there, check out the sculpture of Thomas Beckett, the Archbishop of Canterbury, being martyred in the churchyard. Remember, he's the whole reason Peter was able to get funding for his grand bridge in the first place.
One more stop on the church tour. You may have noticed while you were in St. Magnus the Martyr that St. Magnus was dressed as a viking. I know I wondered "Was he a Viking?!" when I saw him. Well, he was conscripted by Vikings, but, in his saintliness, refused to viking with them. But St. Olaf, who pulled down one of the timber London Bridges, was a Viking, and you can find St. Olave's House on Old Jewry Street, about halfway between St. Paul's and St. Magnus.
To wrap up... this has nothing to do with London Bridge, but I found it an amusing indication of what you can see when you walk around this area today. For your pleasure: a man in a top hat playing a tuba that emitted bursts of fire.