When: Well anytime its warm enough to swim under the waterfalls… I would say between May and September.
Get there: The easiest way to get to the island is by ferry from Alexandroupolis. From there its only a short boat ride. If you stay at “Therma” you can easily walk to the smaller waterfalls “Grya Bathra”. “Fonias” the big waterfalls is a little bit further away but still just a small ride if you have a car. Or you can do what most people do when visiting the island and hitchhike everywhere…
Price: Since Samothraki is in the north of Greece and isn’t the typical “Greek island” like you see in all the pictures about Greece it is cheaper then other islands… However in season I would recommend to book in advance for a good deal. Or stay at the camping which is always cheap. The climbing around the waterfalls is always free of course unless you want to take a guided tour.
Do: Take an entire day… You can climb from waterfall to waterfall and swim in the natural swimming pools. It’s such a great experience. If you’re lucky you’ll end up having a private pool just for yourself. The island has also a couple of beaches, however only one with sand.
My tip: Consider taking a climbing tour at “Fonias”. “Fonias” in english means killer and those waterfalls really deserve the name… whilst you can still get easily to the first and second, going further up without equipment can be dangerous. So if you enjoy climbing just take a climbing tour and get help from professionals. You will even be able to slide some of the waterfalls down.