Unlike in Europe, there are few “Family” Museums in Japan where you can visit and view objects held by one family, accumulated over hundreds of years. This is largely because of major disruptions caused by civil war, earthquake and fire, the upheaval of the Meiji restoration, and destruction caused during World War II.
The Owari Tokugawa family were a branch of the Tokugawa family established by Tokugawa Yoshinao, who was the ninth son of the first Tokugawa Shogun, Tokugawa Ieyasu. They were made Lords of Owari, the western part of present day Aichi Prefecture, and were based in Nagoya.
Following the Meiji Restoration, the head of the family continued as a senior member of the aristocracy and maintained all of the family objects accumulated over 300 (or so) years. This includes an incredible quantity of art and craft objects of the highest quality, armour, household objects, and books and manuscripts.
My favorite objects are the three scrolls of the Tale of Genji (a 12th Century manuscript), suits of armour and swords from the armory collection, and gold and enamel wedding gifts exchanged between the Tokugawa families.
The then 19th head of the family established the Museum in 1931 on the grounds of their historic private residence.
Certainly, some of the major Metropolitan Museums have more objects, but the combination of historical objects owned by one family, and displayed on the site of their residence, makes this my favourite museum.