Take the family to Taverna Kavos for a long lunch, or a relaxing dinner. They're located right on the water. The kids will have fun looking for shells on the beach while you relax and take in the view.
They have a few interesting items on the menu. When we were there, we tried the preserved fish roe, or eggs. We were going to order it, but they brought it out to our table without us asking for it. It was on the house. It's very good with bread.
The other item you should try are the sea dates or steamed striped shells. They're the same thing. These are like mussels except they're longer and thinner with their shells. There's a slight difference with the taste. Sea dates are a bit sweeter.
Sea dates are expensive. But they are terribly hard to find. For example, it is illegal to collect these in Italy. So if you can try them here, I would recommend it.
When you ask for fish here, they ask you to come into the kitchen and pick out your fish. If you do this, bring the kids. They'll enjoy seeing the different kinds of fish.
Last Bit of Advice
While you're waiting for the food, let the kids run around on the beach. It's just in front of the restaurant. It should be easy to keep on eye on them. Tell them to collect sea urchin shells, not the live ones though. There should be quite a few out there in ankle deep water. The shells should be completely smooth without any spines.