Agia Efimia is perfectly located for exploring the rest of the island as everywhere is within 35km drive. There are plenty of bars and restaurants and all are good. I would especially recommend Spiro's for food. For drinks and snacks you must go to Fior d'Amour where you can sit and watch the world go by over a Mythos (or 3!).
Myrto apartments are excellent (although beware if you are going in the next couple of months as there is some building work going on next door!). The beach is pebbly and fairly small but it is good for snorkelling (if you want a sandy beach holiday Kefalonia is probably not for you).
Hire a car and explore. We paid £155 for 7 days in September from Gerolimatos in Sami (they delivered to the door) but Oneira in Agia Efimia itself may be cheaper (they had sold out while we were there).