Zante or Zakynthos as it is properly named is a perfect family destination as long as the area of Laganas is avoided.
There are numerous resorts all around the island and it has many beautiful beaches, one of which is world known as Navagio - the shipwreck.
On the link below you will find many details that may help you decide for your place of stay, but certainly a little touring around the island will be very rewarding.
The island is very green and pretty , and as it was never subject to Turkish control the Venetian influence is still strong there in music and cooking and culture , as is the case in all the Ionian isles .
Avoid the " resort " of Laganas , that is a hell-hole where the chavs and chavettes of the world go to have unrestrained drunken debauches . But the scummy clientele there dont tend to wander far from the place , so the rest of the island remains reasonably civilised .
I am Greek and it took me while to understand you meant Zakynthos. You can't go wrong there. My grandmother is from there and we visited when I was little so I don't remember much detail. I remember the beaches were gorgeous and the night walks around the city with smells of summer and the taverns. It's the best place to go with your family. It's impossible not to love it.
tsilivi is a lovely resort,just enough bars to keep you happy and some of the best food iv'e had in greece.
Its a great place.
Avoid Laganas and you will enjoy your holidays