Anafi lies just east of Santorini, and it feels a world away. There is one small Chora above the harbour, a handful of beaches such as Klisidi close to the port, and a quiet, rugged interior. No airport, no big resorts, and very little nightlife beyond the tavernas: for many travellers that is exactly the point after the crowds of the caldera.
This is the shortest and cheapest way to reach Anafi. The two islands are only about 15 nautical miles apart, and the crossing takes between 1 hr 10 min and about 1 hr 30 min, with fares from €7 when we checked. Compare that with Piraeus, where the direct boat takes many hours, and it is clear why most visitors hop over from Santorini.
The limitation is frequency. Blue Star Ferries and the local Maistros Santorini line share the route, and in last year's data each ran only 2 to 4 days a week. Together they cover most days in summer, but not always every day, and some days have just one boat. Check which company sails on your date before booking a room, and have a plan for your return.
Leave time for Athinios, Santorini's busy main port, which can be congested in high season. On Anafi, you arrive at a small harbour with a beach and tavernas by the quay, and the Chora a short drive uphill.