Just a couple of thoughts. Your ability to drive to Nafplio on your arrival day is totally dependent on your flight arrival time. If its in the afternoon any time past 3 then you probably should go into Athens.
However any time before that you could make that drive. I understand Pats comment about being jet lagged but we have done exactly that. We are full of adrenaline on arrival, that and a couple of cups of strong coffee left us full of energy ( for about 2 hours) before we stopped at a highway rest stop for more coffee. Thus re energized we stopped at Corinth to visit Ancient Nemia. It is just a 5 minute drive north from the turn off to Nafplio. Nemia is not well known ( I think they lack a marketing department) Like Olympia it also hosted the Pan Hellenic games and still has a stadium, a partially restored temple and a very good small museum.
I would suggest you substitute Nemia or Ancient Corinth for Epidavros on this day. The road to Epidavros is hilly and out of the way to Nafplio while Nemia gives you essentially a short drive south to Nafplio.
When you get to Nafplio you will find it is a perfect place to get over jet lag.
All of this is in this album
Nafplio and Peloponnese http://www.flickr.com/photos/stanbr54/sets/72157632094108982/
I might respectfully suggest that your nephew is going to enjoy 4 hours of Palimidi fortress more that Epidavros. Every kids imagination is stoked by a middle ages fortress. You can also take a water taxi to Bortuzi Castle in Nafplio bay.
I like your timing for arrival Delphi. Arrive late afternoon and find a hotel. Take this opportunity to visit the museum so you are prepared for the site the next morning. Do get to the site early. That will give you about two hours before the tour bus crowds arrive. Plan to depart around noon. The drive down the mountain side has a few stops including an absolutely stunning village about 20 minutes from Delphi. I wished we had stopped there.
Plan to arrive Meteora in the early evening. The crowds will be gone and the monasteries will be closed but this is a perfect time to scout out the area. You will also have the opportunity for pictures from perfect vantage points. The next day all those vantage points will be gone by tourists and their buses. Good call to stay at Kastraki its right there.
Olympia Delphi Meteora https://www.flickr.com/photos/stanbr54/sets/72157645469717811/
Not such a good call to plan to drive back to Athens that night. Its a 5 hour drive and you will be tired. We stayed the second night just to regain energy before heading back to Athens.
Athens Central market is an experience. It closes by mid afternoon so morning is a good time to arrive. it is huge. It covers a full block plus secondary stores outside. It is 300 meteru or so from the Monastraki metro station. Find the station look for the acropolis and turn your back to it and start walking. It is on Athinas st.
Images in this album
Athens http://www.flickr.com/photos/stanbr54/sets/72157632121475515/
Now I am going to suggest something that may get me in trouble. On our first visit to the acropolis we arrived right at opening. There was a tour guide sitting on the steps speaking to her tour. We got in and spent an hour at the Acropolis and left when the crowds arrived. The tour guide still hadn't gotten her group through the entrance.
You plan on having guided tours. Thats good plan but a 12 year old may become frustrated by the pace and info overload. Give it a try but if it doesn't work for you just grab a guide book photocopy the appropriate pages so you can do a self guided tour at your own pace. There are also audio downloads on this web site for some of the more important sites.