I was lucky enough to live on Zakynthos for the summer season of 2005 for 6 months.
The island really does have something for everyone. I particularly like the Vassilikos peninsula; hire a car and take the drive down the winding coastal road through Argassi to this wild tip at the point of the island overlooking the mainland of Greece in one direction and Marathonisi, known as 'Turtle Island' in the other. There are some great beaches to visit and pretty views through olive groves at every turn.
My favourite restaurant is La Bruschetta – this restaurant is high above Liminaria (Keri Lakes) for rustic Italian food, al fresco with the most beautiful flowering bougainvillea surrounding the walls of this top notch eatery. Great at sunset! Michaelo's on the Zakynthos Town road is also great. Home cooked traditional Greek food, friendly service and good value. Al fresco restaurant under grape vines. I can still taste the tzatziki! Yum!