One cannot list the Greek islands without mentioning the island of Odysseus if it is indeed the island Homer has written about. The island known as Ithaki is mountainous and rocky but has lots of trees and olive groves, as do the other Ionian islands. Several archeological sites which may or may not be associated with Homer's story along with some beautiful fishing villages and beaches make this an interesting island to visit either from Patras or Kefalonia. Ithaka is an ideal place for walking full of trails and views.Generally the island is small and quiet and June is really wonderful for family vacations.
Vathy (the capital of the island and the place where Odyssey Apartments is located) brings together the northern part of the island which has the best hiking and the southern part has the best beaches (quiet isolated coves, or bigger beaches). The best way to explore the beaches is by boat of-course.
Source: Matt Barret