The City of London — the Square Mile — is the original city, founded by the Romans in AD 43 and walled by the Saxons. Two thousand years of layered history sit shoulder to shoulder with the modern financial district: medieval lanes named for vanished trades, Wren churches rebuilt after the Great Fire, and a cluster of glass towers (the Gherkin, the Cheesegrater, the Walkie-Talkie) marking the modern skyline.
The City is busiest Monday to Friday and almost empty at the weekend — which is, paradoxically, the best time to walk it. With the bankers gone the Roman and medieval bones of the place come through. Wren's St Paul's Cathedral dominates the western half; the Tower of London anchors the east. Between them sit Leadenhall Market, Wren's surviving churches (St Stephen Walbrook, St Mary-le-Bow), and tucked-away pubs like Ye Olde Cheshire Cheese on Fleet Street.
For views, the Sky Garden on top of the Walkie-Talkie is the best free vantage point in central London. The Museum of London tells the city's story from prehistory to the present (free, on London Wall). The lanes off Cheapside — Bow Lane, Pope's Head Alley — are worth wandering for their sense of an older London hidden behind the towers.