Travelling with kids is different than travelling with your life companion only or with friends.
Kids need to be entertained. Athens is full of activities, while the central area of Acropolis / Agora and Hephaestus Temple will be contesting about your valuable time.
If you still have time left in Athens, you may want to include some more "children attractive" activities. So:
The Athens Planetarium
Athens has one of the best planetariums in the world. If planning to visit it, do some king of prebooking, since weekend afternoon shows tend to fill up early. You may want to take a look at:
http://www.athens-today.com/e-planeta...
Greek readers may want to also take a look at:
The Athens Zoological Park
Athens has a zoological Park, located outside of Athens. It has started as a large ( 3rd in the world ) birds collection but gets larger year over year including other species too.
You may want to check:
http://www.atticapark.gr/English/defa...
IME ( Hellenic World Foundation )
This is a children oriented museum - exhibition hall with multimedia presentations. It is a good chance to see something new, presenting historical info on a very children friendly basis. Virtual reality presentations too. Check:
http://www.ime.gr/index_en.html
The Greek Reptile Center
If your children love snakes and reptiles, then give the Greek Reptile Center a try. The center has dozens of snakes on display (including cobras, pythons, rattlesnakes, black mambas, boas, and more) and a few lizards. Unfortunately, the center is not very conveniently located unless you have a car (in which case, it is not far from Exit 7 on the Attiki Odos). Nonetheless, it is guaranteed to be an interesting and educational experience.