Arki is a small island. It has an area of 7 kmē. It is part of the Dodecanese and situated north of Lipsi (Leipsoi). Only about 60 people live here. Since it is almost impossible to get to Arki there is literally no tourism. The only foreigners you'll find here are adventurers with a backpack and sometimes sailors that came here with their boat.
Most of the locals live in the main village Arki. There is little to see and hardly any decent beaches. The little chapel probably worth's visiting but that's it. If you come here to hike the locals will gladly help you out planning the route. Just ask in one of the two tavernas.
Most of the locals are fishermen. Arki now has electricity but no supermarket. There is a little kiosk that sells some basic supplies and as mentioned earlier two tavernas. The dishes are basic but good, prices are average. As you can imagine ordering fish isn't such a bad idea. Unlike other Greek islands fresh fish means fresh and not imported from New Zealand. There are about 20 rooms for rent in Arki. Prices might vary but 20 Euro is a good guess. Don't expect too much. Rooms are pretty basic.
If Arki for your liking is too crowded and big you can arrange with one of the fishermen to bring you to Marati. The island is just off the coast and it shouldn't cost more than 3 to 4 Euros to get there. There is a restaurant on Marati that also rents out rooms. You can count the locals with your fingers (literally) and the beaches are better than on Arki. Go for it!
By the way: The Mount Blanc is NOT the highest mountain in Europe!