Of the 12 original castle towers, the oldest is Inuyama Castle in Inuyama City, Aichi Prefecture. The castle was built in 1537, and although there have been major repairs since then, basically the architecture of that time remains.
I have never been there, but I definitely want to go there someday.
It was designated as a national treasure in 1952, but until 2004, it was owned personally by the descendants of the castle owner. It is now owned by a foundation and is chaired by a descendant (female) of the castle owner.