Hi Christina,
I have visited Nisyros and Tilos approx 5 years ago. Nisyros is my favorite of the two, Tilos was very origin but also with the negative aspect of this (dirty beaches because nobody cleans them and are open to north wind side etc). One night the electricity was cut off for a reason and we could not see our nose but we could see hundreds of stars... and by the way i was the first person in Tilos history that used the bank ec card system because the first bank (maybe still the only one as we speak) on the island opened the days that we were there. So maybe you see my face in the documentary of the bank opening, as the first person celebrating electronic cash withdraws....

If the ec machine is not working then it will be difficult... so for Tilos you should get cash with you (as said stand of five years ago). But try this link, these guys used to run an office that supported tourists with all they needed (info, rooms, cash etc)
http://www.tilostravel.co.uk/In Nisyros accomodation is hard to find i can recall there was only one hotel where luckily we found a room. plain but fine. If there are rooms to let etc these are not shown as usual (could not see any rooms for rent signs) in the capital, Connection from Tilos was at that stage 2ice a week, from Nisyros i think it was daily. Both of the islands are really worth a visit, i am planning to go again at least to Nisyros ... hope you enjoy it.