As a 200 mile long island the island has many interesting features and it really just depends how energetic and adventurous you want to be.
The links below describe the nearest interesting places.
Nea Styra is the nearest town to The Flower House and is where you will probably eat most often and buy your supplies from.
North of Nea Styra there are a number of beautiful places to swim and interesting places to visit including beaches on the Aegean sea side of the island, the nearest of which can be easily reached in half an hour.
South from Nea Styra are some spectacular views and wide plains where the quarries for the green Karystos stone can be seen.