The majority of the accommodation offered in Kefalonia will provide free WiFi access with your stay. Cafes, bars, restaurants and tavernas usually offer free access but make sure to buy something from them. Some areas have poor access due to mountainous terrain and you should expect a slower connection than what you are used to! Still the last few years the networks have been updated and the speeds have raised but we cannot say that it is always stable and can be expected everywhere. A cellular network is always a good alternative and there is coverage in most areas but not everywhere so when hiking or driving through the mountains be prepared to lose the signal from time to time.