If you want to be the only Western Person in sight, then this is a good place to go. Shikoku Japan is situated just under the main island of Honshu but is not as far south as Kyushu.
Getting to Shikoku is not as easy as other parts of Japan, as there is no Shinkansen service to the island so you must use the normal trains, however they are punctual and clean but slower. If you are driving to Shikoku then you will have to travel over one of the 3 bridges which join Shikoku to the main land. All of these are pretty long but if your travelling from the Osaka area then you will have to travel over the Akashi Kaikyo Bridge from Kobe to Awaji Island. This is the longest suspension bridge in the world at 3911 metres long. More information on the Akashi Kaikyo, the Seto-Obashi Bridge and Nishiseto Expressway can be found at the link below.
The largest city is in Shikoku is Matsuyama followed by Takamatsu which is the second largest.
However I have only every been to Kochi which is the third largest city in Shikoku and is quite small by Japanese standards. There are the usual temples and shrines here.
Kochi Castle, Kochi City, Shikoku
Kochi castle is the main castle and is stunning with superb views of Kochi from the top. (Thanks to Yumi for the info.)
Most Japanese visit Kochi for another reason, there is a story of Kukai, also known as Kobo Daishi, a Buddhist priest who brought Buddhism to Japan and founded all 88 temples located in Shikoku, this leads pilgrims to visit all 88 temples on foot, which takes between 40 and 60 days. The pilgrimage starts and ends at Ryozen-Ji near to Naruto in the east of the island and circles the island in a clockwise direction as most temples are close to the coast. Pilgrims wear a traditional Japanese white robe, shoes and a straw hat and collect stamps in a book at each temple. Get all 88 stamps to complete the pilgrimage.
Japanese Paper Museum, Ino Town, Shikoku
Another place to visit in Shikoku are the Japanese Paper Museum in Ino Town.
Here you can make your own Japanese paper, and see a history of Japanese paper making. The factory is a short train journey from Kochi. Worth a visit just to make your own paper, and they will post it too you when its dryed.
Ryugado Caves, Kami City, Shikoku
The caves at Ryugado which are the largest limestone caves in Japan, have a large number of stalactites, stalagmites and some pretty wierd cave formations. They also has the longest outdoor escalator I have ever seen, which leads up from the ticket office to the entrance of the caves.
If your not used to extreme humidity then the inside of the caves might be a bit much for you unless you take it easy. When I went it was 99% humidity and believe me when I say you will sweat inside. On the site there is also a museum which takes you through the various rocks found in the caves, the cave formations, how man lived in the caves thousands of years ago and how the caves where re-discovered, by Dr Hiroshi Yamauchi in 1931.
The caves are about 24 kms from Kochi and are accessable by train to Tosayamada then either taxi or wait for the caves bus to take you the rest of the way. If your going to go by car, then take the Ryugado Skyline which is a windy, twisty road which leads up to the caves from the coast road. Very spectacular views.
In my opinion, Shikoku is one of the more beautiful places to visit in Japan. Its not been touched as much by western culture as other places in Japan and this reflects in the natural beauty of the island. There are no 200ft neon signs lighting up the skies, the people move at a slower pace and the cities are not as large as elsewhere.