Apparently it is hot there at the moment. I did this trip in september. You can go by taxi to Ephesus but it is a long way. They drop you at the top of the ancient site then meet you a couple of hours later when you come out at the bottom. The same goes for the ships trips but they have the bonus of a guide. However Myknos, rhodes and santorinin are beautiful towns and can be reached easily under your own steam. Limmasol needs a taxi or shore excursion as the town is some distance and not pleasant. Ask at reception (not shore excursion desk) for local maps/details of the port. Please do some research on the internet (type in the island name into google and follow the trail !) or go to the library. Check on what there is to see or at least what to look for when you get there IE. windmills in Mykonos. If you cant be bothered - go on the ships trip with the guide !!
I would say that Rhodes and Mykonos are no problem by yourselves but I would take the organised trip to Ephesus and Santorini, there is so much you dont want to miss and the guides on these tours are grreat.
Always DIY - cheaper and so much more satisfying than following the lollipop......lots of sites out there will help you. Try google and cruise ports call boards - the first result.