I would recommend doing a ships tour in Athens. The ship docks in Pireaus and the only way to DIY it to Athens is by Metro or Taxi, approx 25 min ride. If this is your first time and you want to visit the Acropolis - do a tour. Rhodes is easy to walk around, ditto dubrovnik and mykonos.
Be brave just reveiw on the net where you are going then get a taxi,we have done 20 plus cruises and all ways do are own thing .
You do not need to take tours in Rhodes, Mykonos, Corfu or Dubrovnik as the ship is in easy reach of the main sights. In most you have to be able to walk about a mile or at most two but at your own pace.However if you want to see Ephesus (from Kusadasi) which is wonderful then take an organised tour. Similarly if you want to see the Parthenon in Athens do the same (although be warned the walk up to the top is steep and tiring, especially in the heat). Alternatives for Athens are organised trips to Corinth or Cape Souinon both of which are good and not as tiring and you get a good coach ride to see the Greek countryside included. From Katakolon one can get to Olympia but I found this very disappointing and an alternative is to walk into the village of Katakolon from the ship (5 minutes). This is made up of bars, restaurants and shops plus a beautiful church at the end of the main street which is worth a visit. You may find this far more relaxing.
Do not always take the advice of those people who are mainly intent on economy over convenience. Yes the organised tours are expensive but you walk straight onto your air-conditioned coach, are door to door and have your own local guide who can bring the tour to life. Additionally you do not have to worry about timing and getting back to the ship. Yes all the clever joes will tell you how they have been cruising for 20 years and the best way is to go on your own and not on 50 seater coaches but for some people they are the answer - especially if you are able to afford the price. We have done both and still do so but there is no black and white answer and to start with I recommend at least a couple of the organised tours.