A beautiful and spacious (outside of rush hour) way to get from Highbury, through east London to south of the river in minutes. The train snakes epically through Hoxton and Shoreditch and opens up the Jubilee Line via the beautiful Canada Water / Bermondsey stations.
Maybe an obvious choice, but the Barbican is always good. My favourite space in there is the curve gallery, last time I went was for Cory Arcangel's 'Beat the Champ'. I love the architecture, although not many people do. I think it was voted 'London's ugliest building' in 2003.
This is my favourite place to have a morning coffee in London. Its real chilled and the music is always perfectly set to welcome the day in, its usually something I have never heard before too. The coffee is good and the tip jar they have is the best tip jar in the world so make sure you bring a bag of pennies. Sit with your sketch book and have a lil think.
As a keen runner, running through Greenwich Park and on to the river side I see the Thames Barrier, which is not only the worlds second-largest movable flood barrier (after the Oosterscheldekering in the Netherlands) but is also an iconic site on what is fast becoming a recognised stretch for developers including the 02 and Ravensbourne College of Design and Communication.