It really depends on what specifically you are looking for in an island (Quiet Beach, Party, History, Scenery) then beyond that, what time you have and transport options. The common mistake people make is to pick out a list of islands, then find that getting to each is nearly impossible, or requires repeated backtracking through Athens. Most wind up opting for islands that are on a common ferry route (Mykonos, Paros, Santorini, as the previous poster recommended).
In regards to your pick, Ithaca, I will point out that it is over off the Western shore of Greece, well away from the Aegean and what most think of the "Greek Islands". If you are interested in Ithaca, consider other islands in that group, Corfu and Zakynthos are two more that come to mind.