You can hire a safety deposit box from most of the hotels. If you are staying up the end where The Ark or Two Brothers bar is (as we did in June) The Mediteranee Hotel is as good a place as any. The cost was 20 Euros per week, which I thought was'nt too bad (compared with the cost of what it would mean to retrieve your stuff once it had been nicked or lost!! Trust me, We met a couple last year who had their stuff nicked the second day they were there. Spent four days having to go to Athens for passport renewals etc, borrow money off friends because they'd gone independantly, arrange everything themselves, it was a nightmare and must have cost them loads!! Then you have the hastle with the insurance when you get back!!
Honest, 20 Euro's is nothing.
Hope this helps