The Tate Modern is utterly fantastic! The best part is the Turbine Hall-the huge hall which usually has some kind of installation art piece, often interactive. I’ve seen some really amazing mind-blowing art there-and the Turbine Hall is free! The rest of the museum may or may not be worth it, depending on your tastes in art, but if you’re in London, at least pop your head into the Turbine Hall to see what’s on.