Walking around (or even biking) is one of the best leisurely wats to get to a know an island in Greece. That's why I love to visit Greek islands, is because you usually won't miss anything because everything is so quant and small and walkable. If anyone has any advice about the island of Kefalonia, I would love to know. My best tips that I have to visit in Kefalonia are Katovrahes and Melissani cave.
The Castle of Assos is an old Venetian fortress that has been left over from the Italian occupation of the island. Today, it is a beautiful pile of ruins that tourists can visit and learn about the history of Greece. You can hire a guy to take you around the different parts and explain the history, but I don't really recommend them as most of the information is available online if you're willing to do your own research. Please let me know if you've ever been! I would love to learn about what you thought of the castle.
Ammes beach is in the Svoronata area which is very close to the airport. Its about 10 km southwest of Argostoli and one of the best beaches on the island! It's a pretty low-key beach with some great organized lounge chairs but as with most beaches in Greece, you can find a public spot where you can swim with ease and free of charge. The beach is super sandy and the waters are very clear. I highly recommend it!
Mandola is a very popular sweet in Kefalonia and it is one of the biggest exports from the island. This treat is made of almond, honey, sugar and egg whites. The dessert has a few different variations, but is usually gluten free! The ingredients are very simple which is why they are so allergen friendly. I was doing some research and apparently these cookies are originally from the Venetian occupation in Kefalonia.