We have stayed in Kefalonia twice. last year at Aghia Efimia which we really enjoyed, it is quiet, no shops, well a couple, and about 10 tavernas, it would be very safe, the beach is pebbles but lovely clear sea. may be too quiet for teenagers though. Skala I would also say would be safe, more bars and tavernas, places for them to wander about. there are shops too but it is still not a noisy resort.

I echo the last post, Skala is a nice balance, several bars giving the teenagers a bit of independance without them being in a large football shirt wearing lager lout environment. there are not any clubs etc... just lots of nice tavernas and nice more upmarket bars, served by on the whole nice well mannered pleasant waitresses.

Lassi is a bit like blackpool, amd all the other resorts are very quiet beautiful places.

HTH

But no curry houses for the currymonster

While i agree Skala is a great resort, for teenagers it may just be a little on the quiet side, especially if you are not hiring a car as public transport down in Skala is virtually non existant.
Lassi may well be a better option as it is more centrally placed with the capital Argostoli just a stones throw away.
Lassi is not a personal favourite of mine but it gives you a few more options for seeing things if you are not hiring a car. If however, you are taking in a few excursions such as the island tour, then i would definately say SKALA!

We are off to Kefalonia again in May been going since 1989. we always stay in Lixouri but as it is not in a brouchure anymore we have to travel flight only but we are in our 60's and this place is ideal for us. Maybe Agostoli would be a good base, you are near the local bus service where you explore many parts of the Island, get the ferry over to Lixouri just 25 minutes sail and very reasonably priced, seems to be plenty of nightlife with good restaurants and bars, don't know about disco's for the children in Lixouri they are well out of the town.
But Kefalonia is a beautiful Island with plenty of places of interest, some lovely beaches. hope you enjoy it as much as we do.
pojo