The Household Cavalry Museum
The courtyard itself is well worth a look in (since it's free), even if you're not a tourist. The horses and guardsmen are all really friendly. If you encounter a member of the Household Cavalry while they're not on official duty (such as if you're lucky to be there on a social/promotional event), then they are all really splendid, genuine, heartwarming, and friendly people. This is the unit that form the guards in front of Buckingham Palace, so the people that do this job are happy to talk about how it works, what they do, etc etc. There is a museum on site giving the history of the unit in general as well as outlining it's modern day duties. Well worth a visit.