There is a bus service in Tilos which gets you around the islands paved streets quite well. Schedule is posted on the main square and in the menues of most restaurants. Fares 1.20 Livadia-Eristos, short distances 0.60 2009.
There are also a few car and motorbike rentals. Watch out, some of them don't cover any damages to the vehicle if you drive on sand roads, which are half of the roads of Tilos ;-) Shop around for the best prices.
