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.
Getting lost is an age old suggestion but a good one. Put away your cell phone or your A-Z and just wander around. I still do this regularly even though Ive lived here for nearly 10 years. London is a big city and it drip feeds you its secrets sometimes. You will come across things you wouldn't usually, in amongst the Starbucks and pret a mange there are some amazing sights. Just 'being' somewhere is a great experience and one no guide book can help you find.
The power station is a ghost like ruin that stands on the banks of the Thames. Its right next to the train tracks rolling out of London to the rest of the south of England. I pass it every time I go back to where I grew up and every time I arrive back in London. It has become symbolic with arriving and departing, a constant in my life. I used to joke and refer to it as my lover - seeing me off and welcoming me home.
Spring always arrives earlier to London, and London shows its most beautiful face during the spring. If you live in London, or if you come to visit, bring your training shoes and take a morning run along river Thames in Chiswick. Between Barnes Bridge and Hammersmith Bridge, there's a great trail on both sides of the river. And if you take the run in March, you might run through this wonderful Alice-in-Wonderland cherry-blossom landscape.