It was my first time on Kefalonia (so far I visited Corfu many times, Zakynthos, Cyprus, Rhodos, Crete, Athens, etc..).
Kefalonia was highly destroyed during 1953 earthquake so do not expect ancient ruins or old towns (some exceptions, see below). Many towns have been rebuilt after 1953, still they have some nice places to go or visit.
In general, Kefalonia is a very nice, slow-life, slow-speed, place to relax :-), with rather some natural beautiful views than ancient places or live cities (like Corfu capital).
Here's a list of some of the places I've visited myself and some short description:
* I stayed at the resort at the Xi beach. Xi beach is long, sandy, sometimes quite narrow (or very narrow if it's windy) but it's one of the best on Kefalonia i my opinion. Shallow warm waters and some natural clay for body :-).
* Lixouri - some small sleeping with with a great ficus tree in the center of its market in the city center. One small shopping street but even during high season in July/Aug it was rather sleepy and quiet. A couple of restaurants around ficus tree and market to sit down and relax. Rather very quiet town
You can take a ferry, every half-an hour to transer yourself and family to Argostoli, capital of Kefalonia
* Argostoli - not that bit as one might expect still lovely capital of Kefalonia. One main shopping street (quite long), closed for cars, with cafes, shops, restaurants. If you want to buy clothes, I would rather suggest Fiskardo at the north of Kefalonia. Argostoli was rebuilt after 1953 so do not expect old ancient houses or ruins. Still have a walk at the port and make sure to come there at around 8-11 to see live Careta turtles ! - they swim right at your foot !
Enjoy the De Bosset bridge and the views from there.
* Fiskardo - a small town at the north of the iceland which was not devasted by the earthquake in 1953. Quite busy town, with lots of ships arriving, departing, couple of nice restaurants, and a few boutiqes to buy clothes - reasonable prices (lower than in Argostoli !) and good quality
Kefalonia has several places with great views and beaches.
The most famous beach is Mirtos, considered one of the best in the world. Well, definitely the views from the road (especially if you drive along the west cost from south towards Mirtos and further to Fiskardo) are great and spectacular. Keep in mind that Mirtos is not a sandy beach, but with it's white small stones creates spectacular views. Go in the morning to secure your place as it might get crowded during the day.
Xi beach - I mentioned above, great to come with kids, there are several places to stop there and the white/grey cliffs at the south-west are great and picturesquee. Go to Kounopetra beach or view point to see the full cliffs, or Xi beach to beach right beneath the cliffs
Personally, I liked the Petani sandy beach. Not very big but quite wide and long with great taverna (the very one at the center of the beach). Pick windy day to enjoy spectactular (even 2m high !) waves to have fun :) !
Ammos beach - this one is closed because some rocks destroyed some of the 400 steps which led towards the beach. It's similar to Mirtos, fantastic view, looks sandy but there's no way to get to it. You can go by car to the last parking (road is OKish most of the time, except around 50-80m which might be tough for family car) and then enjoy the view from the cliff above.
The Scala beach is in my opinion overated. Yes, it is sandy, it is wide and very long (3km ?) but it gets deep very fast so not very good for small kids - go to Xi and kids will love it.
Melissani lake is probably #1 place to visit on Kefalonia. Well, it's a lake which was hidden in the cave. Now the roof is open because part of it collapsed in 1953. Still, crowdy place but definitely give it a try. After probably a long queue (it moves quite fast) you go down thru the stone corridor straight to the lake and the boat. You cruise for around 10-15min and that's it :-).
Personally I liked more the Drogarati Cave which is just a few km away from the lake. Cave is quite big, with lots of stalagmites and stalacties but no-one is pushing you to move along so you can spend there as much time as you want. It's not that cold inside as some might say. Shorts and t-shirt was fine for a 20-30 min walk around.
Itaka - we decided to take a boat tour around Itaka to see that corresponding iceland as well. It was a nice day, with 2 stops for swimming and 2 stops in small cities of Itaka.
Vathy, capital of Itaka is a small town with a nice port and a 3-4 tavernas. Take the steps to the church above the city to see the panorama !
While crusing around Itaka, it came to light that the iceland does not realy have such great views as Kefalonia. On the other hand, there are no big hotels on Itaka, so you if you want to escape from crowds, people, etc and just read books, it might be a nice place for rest.
In summary, Kefalonia, appeared to me like a nice place for a family rest. Slow life, some spectacular views, a couple of great beaches, Careta turtles :-), and, if you want some interesting wine (Robola - you can visit a winery not far from the Saint Gerasimos Kefalonia Holly Convent, and taste it for free).
And you can see the whole iceland from the Ainos top but take better shoes to get to the top (sandals might be risky).