Shikoku Island, which is accessible via a bridge from the mainland, or alternatively via ferry from other smaller surrounding islands is a stunning location to explore, with breathtaking sights.
As usual, the further you get away from the city areas, the more beauty there is to see. Being the 4th largest island of Japan, there's too much to list here. There are many possible activities and sites for you to savor & discover.
Naturally, being surrounded by ocean, there's great seafood to eat, especially in the coastal regions.
There are great beaches too and part of the adventure is in exploring and finding them.
We recommend consulting Lonely Planet for more detailed suggestions.
Remember there are also other islands where you can inexpensively travel to. Our personal favourite is Shodoshima, for its beautiful deserted beaches and snorkelling, or great views from the higher regions, from where you can find lots of views to watch great sunsets from
Shodoshima is also well known for its olives!