We’re not really sure what you would be interested in doing if you stay in Nafplio. It’s certainly a good base for visiting Epidaurus and Mycenae and a good first stop if you’re planning to explore the Peloponnese. But if you only spend one night there, you’re not really going to get much out of your stay other than the round-trip drive from Athens. So, in my opinion, just like Tommy, I don’t think it’s really worth it. You could just as easily spend those 2 days enjoying Athens instead.
As for staying near the airport, There aren't really any worthwhile hotels near the airport aside from the Sofitel right across from the terminal, which costs around €300 a night.
With all the other hotels that are more or less close to the airport you’ll be in a pretty uninteresting suburb with no real services, restaurants, or anything else nearby, and you’ll still have to pay for a transfer of at least 15 minutes to get to the airport. So there’s really no advantage to staying near the airport instead of staying in Athens even if you have an early morning flight.
We often have flights out of Athens around 8 a.m., or even earlier, and all you have to do is pre-book a taxi. The drive early in the morning takes about 40 minutes. So, basically the only thing you’ll gain by staying near the airport is about 20 extra minutes of sleep in a place where there’s really nothing to do.
I gave you some suggestions in response to your other message. You didn’t like any of them?