I've been to several places in Greece, but I liked Zakynthos especially. I stayed in Argassi, which is a nice little resort, not too crowded, not too loud. While Argassi does have a small stretch of sandy beach that was good enough for a swim, we really enjoyed renting a car (or a quad), wander around the island and do beach hopping.
1. Dafni
We rented a car around 8am that day and got to the beach before 9am. There was hardly anyone, the surroundings were wild and green, the water was warm and crystal clear, the pointy cliffs were covered in mist. It was magical. There's a few beach bars and restaurants nearby, and it's especially nice and quiet during the weekdays (more locals gather around in the weekends).
Daphne was my favorite beach in Zakynthos and apparently it boats the warmest water temperatures of the island. The wide, long strand of sand is a protected area for the sea turtles, Caretta caretta. Early morning they come here to nest and you can spot them right before sunrise. Visitors are asked not to touch or disturb the turtles or the nests in any way.
2. Navagio
It's in all the tops of best beaches in the world (according to CNN and others) and it's probably Navagio that you'll see every time somebody posts photos related to Zakynthos. It's indeed beautiful. The white pebbles and the incredible shades of blue are hard to describe in words. You can only get to this beach by boat, as it's surrounded by limestone cliffs. Also known as the “Shipwreck beach”, it's got a stranded Freightliner on display. The ship was used to smuggle cigarettes and, on a stormy night when it was chased by authorities, it ended up on this beach and never left.
While it's beautiful to behold, it's less cozy for doing actual beach activities. There's little sand, mostly pebbles; there's not a lot of natural shade, so it gets incredibly hot. Also, there's so many tourists and boats coming in, it gets really tiresome. You can hardly find a peaceful moment during the day.
3. Gerakas
Another wild beach, Gerakas is sandy, so it's pleasant for turtles and people alike. You're not allowed to enter the beach half an hour before sunset and half an hour after sunrise, as it's also a protected hatching ground for turtles.
4. Porto Azurro
With pines, sunshades, sunbeds, pretty beach bars and rocks in the blue water, this beach is more on the elegant side and apparently popular for wedding receptions. We got there on a rather windy day and it was probably the only time we got big waves in Zakynthos.
5. Makris Gialos
A smaller beach with very clear and deeper waters. Not too crowded generally, it doesn't have too many touristic facilities, so make sure to pack up drinking water at least. Very close by, there's also Xigia beach, that has natural sulfur springs flowing into the seawater. People bathe there for the therapeutic benefits of salt and sulfur. You can probably imagine the smell, too.