Alexandra, I have just returned from a Greece visit (my 13th since 1999) to these 3 exact destinations, two of which I've visited on every trip, and the 3rd, Nafplio, about 9 of the 13 trips. So I believe I've found the most effective way to maximize time on-site,enjoying, while minimizing transit time and avoiding backtracking. NOTE: since it involves domestic flights it would have been helpful to have exact dates because the most suitable Naxos flights even this far in advance may be sold out (one reason Naxos is such an enjoyable island is that its airfield cannot accommodate jumbo jets, just v. modern turbo models seating 40).
I recommend altering your sequence, doing Naxos first, then flying back to ATH, renting a car for visit to Nafplio area, then returning for final days in Athens. This exact sequence is what we did from June 3rd thru June 17. Here's the way it would work:
DAY 1 -- Arrive ATH noonish; 1st available flight is then 1600 - arr 1640 (3-3:40) Airport is VERY close to port town & its adjoining beach area, Ag. Giorgios (St. George). I recommend the latter, rather than farther-out beach areas, which are great for swims but in eve in Sept are more closed-down. St. G. is serene by night, but also just a 15 minute stroll from beach to the lively town seafront crescent of cafes, tavernas, shops etc. Believe me, I've stayed in many areas, and have found this the most enjoyable. With luck, you can be in swimsuits and having a dip shortly after 4 pm! Sun goes down about 7:30 -- enough time for you to walk to the famous Arch on the harbor islet for the obligatory foto thru the arch! A good start to your stay. I can recommend hotels.
DAY 2-3-4 -- Allow one morning just to explore/enjoy the fascinating Port Town, climb up to its Kastro (Castle) see the amazing tiny museum with world's top collection of pre-Minoan statues, walk the winding maze-like lanes... then take bus near ferry pier to visit gorgeous PLAKA beach to swim. One day, rent a car to zoom around the island's highlights: hillside villages, ruins, marble mountains, more (or you can hire a guide for this)
DAY 5 - FLY in AM back to ATH (Here's where I wish you'd given dates; on a few dates there's still seats on the 10 am flight arr 11:15; otherwise you'll have to get up early for the 7:25 - arr 8:10. book NOW). Get rental car (I highly recommend Athens Car Rental), drive to NAFPLIO...2.5 hours if you go nonstop. En route, after crossing Corinth Canal, I highly recommend short stop at ANCIENT NEMEA -- just off the big intercity highway.... a "Sacred Games Site" runner-up to Olympia; a real thrill you can see in 45 minutes. I STRONGLY recommend Hotel Agammemnon both for location nd value, if you can snag one of the rooms directly on the seafront with water-view balcony.
DAY 6 - 7 -- 1st day to explore this glorious Old TOWN, 2nd to visit Nearby sites; for the BEST overall guide to Nafplio & area, use http://www.visitnafplio.com and believe every word; its creator is THE best, and totally noncommmercial. Day 1, walk old town, go to Acronafplia, walk around point at waters edge, swim @ cute tny town beach? Day 2 - on such a short trip, don't attempt Mycenae, instead visit nearby TIRYNS, then drive up back of PALAMIDI fortress (or taxi); walk down the 999 steps.?
DAY 8 - Leave early, no need to backtrack -- instead drive across "thumb" of Pelops to EPIDAURUS; don't spend hours on acres of ruins, it's mainly about the stunning Theatre. Then you can drive up the coastal Road to Isthmus and stop by the Original bridge to see & photo the Narrow, Deeeeep canal. Then hop onto the big intercity highway to return to airport by 2 pm or so... taxi @ flat-fee €38 to Athens hotel. If not exhausted, u could go up on Acropolis @ 5 pm... NO crowds, beautiful golden late-day light.
DAY 9 - 10 - 11 -- Enjoy the cultural and landmark riches of Athens. I dont recommend a one-day bus tour to delphi -- too rushed.