Shikoku is the smallest of Japan's four main islands has the oldest hot spring in Japan (Dogo - said to be 3,000 years old). It, reputedly, has the best noodles in Japan too!

There is a special section of the Shinrokaku onsen (at Dogo) set aside for the imperial family and the existing buiding was built in 1894.
Matsuyama castle is a popular place to visit for cherry blossom viewing if you happen to be there in April.

Not sure which area you want to go to? For more information, check out the links below.