Very pleasant tree-lined road which connects Hyde Park Corner with Buckingham Palace and thus The Mall. Part of a well-known shortcut into the heart of the West End and towards the City, although it is closed on Sundays.
As its name implies, it's a hill - but a very gentle one and particularly easy to cycle along as it has a shared-use pedestrian/cycle path along the [Green Park]? side.
Constitution Hill runs between [Green Park]? and Buckingham Palace Gardens (which, naturally, is behind a big wall).