It is not smaller nor out of the way, but the New Tate is not to be missed.
The readaptive architecture is outstanding and several of the exhibits mixed the modern with the traditional.  Also, the view and food from the restaurant at the top of the museum looking out over St. Paul's and the millennium bridge is well worth your time.
I also recently enjoyed Chartwell, Churchill's home which is on the National Trust list.  You might look at the NT website for other suggestions of homes and gardens.

Susan J. Floyd