The V&A is the national museum of art and design, and its collections are extraordinary in their range: Islamic ceramics, Japanese swords, Renaissance sculpture, the Great Bed of Ware, entire rescued period rooms, a cast of Trajan's Column. It's the kind of museum where you wander in looking for one thing and emerge three hours later having been sidetracked by a dozen others. The café is also genuinely good.
Cromwell Road, South Kensington. Open daily. Free admission.