Take the kids for a boat ride in the Melissani Cave.
The tour will have you and the family getting into a larger row boat with a Greek guide. The guide will do the rowing and tell you about this interesting natural wonder.
It's easy to get onto a tour. Just walk around the outside of the gift shop until you see the ticket booth. After you get your tickets, you'll walk down some stairs and into a corridor cave heading down to the "boat landing."
The guides will then help you and the family get onto a boat.
The tour only lasts about 15 minutes. You'll probably end up spending more time in the gift shop then on the tour. None the less, it's different and interesting.
Last Bit of Advice
If the kids want to jump into the water after the trip, just drive north, along the water. Drive slowly and watch for places to park. You'll see spots, just for one car alongside the road. When you find a parking spot, look to see if there is an easy path down to the beach. You should be able to find your own private beach. It will be a private beach because some of these spots are so small, they will only fit one family.
If you're looking for lunch, To Steki Taverna is a nice place to eat at that's just a bit north of the cave.