London - The Tate Modern is one of the most intriguing and interesting museums in the world. It is a must see, both for its setting (along the Thames, housed in a huge defunct power plant) and its installations and stationary art collections. It is free of charge and has marvelous (and not too expensive) museum stores to shop in.
Cold Dark Matter: An Exploded View by Cornelia Parker. Saw this at The Tate Modern, London and completely fell in love with it. There was so much to see in the actual exhibit and the single lightbulb lighting the room made it almost feel magical with all the shadows on the walls.