There is one in Oia next to the bus square. It is usually clean but bring your own toilet tissue. You have to pay for the WC's at both Oia and Fira bus stations (0.50 cents). Like Bigsnitch says, I'd try and avoid the Fira one as its a squat-style and usually not the nicest (grubby).
Can you put toilet paper in toilet in Crete?
This may come as a shock to many, but you are not supposed to flush toilet paper down the toilet in Crete. This is true in all Greek islands and most cities in the country. Greek sewage pipes are too thin to handle any amount of toilet paper.