1.transportation from Athens to Napfilo and back
For Nafplio the best is to rent a car. From Athens downtown or Athens Airport you will be there in less than 2 hours.
Last May, in Nafplio we stayed at
Chara's studio under Palamidi castle. It can accommodate 4 people.
It's not in the old town but that was on purpose. It's a 15 minute walk to the old town and there are some good restaurants close by which are less of a tourist trap than those in the old town.
https://www.airbnb.com/rooms/36868281?
The trip Athens → Delphi takes 2h30 minimum by car and 3 hours minimum by bus, in my opinion that's a lot of travel time for not much time on site.
I usually have a flight around 8am from Athens and I always stay in Athens the last night.
Leaving around 5 a.m. the journey Athens → Airport takes about 45 minutes by taxi.
Why would I change accommodation and go get lost in an uninteresting suburb just to save 15 minutes by being closer to the airport? So I can enjoy one last evening in Athens.
Especially since if you have to change accommodation you will have to check out before 11am, it's not just one evening that you lose but almost the whole day.
That being said, there is the Sofitel hotel at the airport. you are 5 minutes from the check-in counters, but the price of the room is over 200€.