The island is not too big so you could have a walk on the narrow streets and buy some souvenirs for the loved ones.
However, we were disappointed by the sights: because of the great reviews it receives on the internet, our expectations were high. In fact, the island is just two small villages that do not have anything extraordinary that you cannot find somewhere else in Italy.
We did not have the time to also take a boat tour around the island to see the sea caves and the beautiful blue sea. Probably that would have been the better choice to spend the day, than to walk around on the island.