In planning a visit to the Dodecanese, keep in mind that Rhodes has the longest tourist season. So if you're rushing into the season in April, begin in Rhodes; if you're stretching the season into October, end up in Rhodes. In any case, if you can, avoid the Dodecanese July and August, when they are so crowded that they nearly sink.
In high season, at least, you can travel easily from one to the other of the three principal islands described here -- Rhodes, Kos, and Patmos (although the excursion to Patmos really requires a minimum of 2 days). From the mainland, all are best reached by air. Rhodes and Kos have airports; Patmos is a short jaunt by hydrofoil from Samos, which also has an airport. From Kos and Rhodes, you can get just about anywhere in the eastern Aegean, including nearby Turkey, which is worth at least a day's excursion. Simi can be reached by ferry from Piraeus, but most people will approach it by boat as an excursion from Rhodes.