Before there was London there was Londinium, and around that settlement was a protective wall - the London Wall
Now, of all the places to visit, you may not find it high on your list of priorities to go to part of a long-since-near-totally destroyed defensive wall, which used to mark the boundary of the city of London (in fact there is a street of the same name which follows part of the route of the original wall within the City.
Probably best visited on route to the big attractions nearby - Tower Bridge and the Tower of London - it is still worth pausing to reflect for a moment or two at what has happened in and around this fragment, and imagining if there had been such things as CCTV way back in the days of its construction, what changes you would have been able to see.
The fragment to look out for is located very close to the entrance/exit to Tower Hill tube station, and is easily recognisable due to the statue of the Roman Emperor Trajan positioned in front of it. There are more fragments remaining, however, should this not be enough. You can see a decent section in the Barbican area for example, and another part within the Museum of London. Should you want to get a feel for the London of old though, stand by the Emperor and peer out across to the Tower of London, then to the river and imagine what it would have been like to be a Roman soldier at the time - with none of these oh-so-famous monuments there at all, just land and the flow of a river - maybe then you'll see London, and all that has changed in it over the last 2000 or so years in a slightly different light...