Although not one of the 12 castles in the original form, an interesting example and a good place to visit is the Gifu castle, located on Mount Kinka at a height of 300 meters over the surrounding area. There are many interesting artifacts on display (especially related to the famous Oda Nobunaga) and the 360-degree view from the top of the castle is wonderful.
The steep climb takes about one hour by foot, but there's also a ropeway that will take you there in just 3 minutes...
EXIF info:
Nikon D700
Lens: 24-70mm F/2.8G
Focal Length: 24mm
Aperture: F/7.1
Shutter Speed: 1/400s
ISO Sensitivity: ISO 200