Many years since we have been to Zakynthos, we hired a couple of mopeds and went around the island, I remember stopping in Argassi and going down to the beach which was a nice spot with nice clean sand and a strange little stone bridge thing that didn't seem to serve any purpose.
It isn't a wide beach and is a mix of sand and shingle as you walk along it, the water is quite shallow at this point.
We loved Zakynthos and stayed in Laganas before the 18-30 types moved in, as I said we haven't been back for several years and I would love to hear what you though of it when you return.
Have a great holiday
Graham