Kefallonia was the first place I went to in Greece, about 1984! Been back a few times, and though it has gotten busier, it's still a lovely island.
Argostoli is the capital. Bustling working port, good town square with restaurants and bars. Stayed there first two visits, Hotel Aenos (!) Good but can be noisy of an evening as its sat right on the square.
Lassi is the main resort. Two great soft sandy beaches, now surrounded by hotels and apartments, also bars and tavernas.
(Was two hotels, and an old wheeless van on the beach selling gyros and beer first time I went, lol)
Fiskardo, right in the north is the 'posh' bit. Loads of big yachts and boats in the harbour. But is a lovely town too. (one of the few not badly damaged in the big earthquake in the 50's, so great old buildings still)
Skala, Assoss and the other resorts are smaller, but just as nice.
Check out the underground lake at Mellisani, and the Drogorati Caves. Fascinating.
A great holiday for couples and families, but not one for anyone wanting Aya Napa, or Faliraki!