Mansion House is the Lord Mayor of London's official residence. Its rooftop is where Jacob meets Abberline at the start of A Bad Penny, before the Bank of England heist.
After the Great Fire, the City wanted a single home for its mayors, who had worked from their own houses or guild halls. Sir Crisp Gascoyne moved in in 1752, before it was finished.
Abberline waits on the Mansion House roof, pipe in hand, when Jacob arrives to plan how to stop Philip Twopenny robbing the Bank of England across the road. From there Jacob goes into the bank, joins a tour, peels off to tail the manager and the head of security, and gets the vault opened. He hides behind a painting inside and kills Twopenny through it.
Bank of England
The Bank of England is the City of London's central bank and the target of Sequence 6, A Run on the Bank, where Jacob tracks a Templar robbing its branches. You return to its vault twice more: once for the stolen printing plates and once in The Last Maharaja.
City of London
The City of London is the borough of banks, trading halls and tall stone offices on the north bank of the Thames. In 1868 the Templar Bloody Nora runs it through the Blighters, and you take it from her by clearing her lieutenants, strongholds and factories before a final gang war.