The Design Museum is in an old 1950's warehouse, with a Bauhas-like conversion and decor. Its exhibits include an unpretentious display of mass-produced items from industrial design products down to Tupperware. They also hold exhibitions on particular events, movements and designers, and have a shop that sells many items. Admission fees apply and concessions are also available.
I've been here a couple of times for some wonderful and varied exhibits. First time was for the Peter Saville exhibit, showcasing the work he did for Factory Records and some Japanese design magazine among other things. They had samples of materials he used for his shoots, including the leaf from the True Faith 12" and some of the materials that inspired the early Factory sleeves.
I've also seen a Saul Bass exhibit there, showcasing the man who did most of Hitchcock's opening title sequences among other things.
They also have more off the wall exhibits, like the chair exhibit I saw, as well as an exhibit that was basically the history of video games, complete with then-current consoles available to play on.
They also have a shop where you can buy design related books, as well as merchandise related to current exhibitions. They also have a nice little cafe.