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.
The Greenwich Observatory with its green laser beam can transfigure any night sky. If you decide to cross the Thames via the foot tunnel, make sure you look out for the green ray. You can be on one side of the meridian in a minute, and cross to the other side on the next, without even realising it.