Good Greek food in Athens ?
I have never seen a family with children not to be welcomed anywhere in Greece.
You can try the GB corner in Syntagma square,(the most central square where the parlianment is)mainly for the food or now that the weather is hot you can to go Plaka or Thisio, mainly for the location. There are many restaurants with their menus posted outside. I have tried the restaurant Kuzina which was good.