Visiting Athens, Nafplio and Naxos. What order?

Full disclosure, we drove to Nafplio upon arrival, even though at 2.5 hours, that is the absolute max we would drive after an overnight flight (from US east coast). My husband is the driver and he felt confident that would be fine, and it is an easy drive (highway, then some rural roads). If you have any reason to think you would not be fine to drive, then of course don't, but if you don't find any other flights to facilitate going to Naxos first, then that is what I would recommend considering. It is really not inconvenient, especially when you consider that you can stop at places like Corinth or Nemea in between Athens and Nafplio.
I do not know the recommended wait time to have between ATH arrival and an island flight, but your flight could always be late, so that would be a bit stressful to me.
We went in late May last year and it was an absolutely perfect time to be there--resplendent weather, nothing too crowded.

I think landing and heading to Nafplio works well. We did this and didn't find the drive onerous at all. Nafplio is a good place to get acclimated to Greece and get through jet lag. We also went to Naxos. I think the pace of Nafplio lets you down-shift some, and then in Naxos you will downshift again, before revving back up in Athens...

I agree it's a good sequence. One trip I did, we landed in AM also & used that sequence; i wasn't driver, but our driver was up to it & it was easy. Modern multi-lane highway nonstop til after Corinth Canal, avoid Athens traffic entirely. Check this fab online map http://euro-map.com/karty-grecii/peloponnes/podrobnaya-turisticheskaya-karta-peloponnesa.jpg (click & it gets huuge; navigate w side-slides)...it shows how easy the "big Green Road" is.... also of your options for efficient site-seeing, e.g.

• Just about 10 mi. after Corinth Canal, u can exit RIGHT for about 5 miles & stop at Ancient NEMEA for a break... it's like "Olympia wannabe" with ruins, temple columns, swell stadium with athlete's tunnel & race startng-blocks ntact (in July they're running the 4th Nemea Sacred Games Revival!). Plus NO crowds. Stop for a snack? in Nemea village... right on main St there's a winebottling shop -- u are in heart of BEST red-wine country in Greece IMHO. Cross over (under?) big highway & u are on road to Nafplio, curving among citrus Orchards & olive groves.

• Mycenae & Tiryns & Palamidi etc fun to explore while in Nafplio... and you can avoid backtracking by doing Epidaurus on yur drive BACK to the airport... Leave in AM, Drive across the Peloponnese "thumb" (see map) to Epidaurus... don't waste too much time on acres & acres of badly-signed rubble, the awesome world-famous theatre is the MAIN thing. Afterward, just continue East tothe seafront road & go north. When u get up to Isthmia, you can connect to the "big green Road" again... in Isthmia you can stp by the "old bridge" over the corinth Canal for a few minutes, just to gaze (so deep so skinny!) take pix & move on. Only thing to remember in the whole easy inbound drive is -- when you get near the Fork in the Road (at Elefsina) turn LEFT!! which goes right back to Airport. Right turn gets u into a hellish route to Piraeus.

Thanks for those helpful replies! We will go with Nafplio, Naxos and then Athens.

We’d also like to visit Delphi, and can stay overnight to visit in the morning to avoid crowds. Would you recommend stopping there at the beginning or end of the Nafplio part of the trip? Or as a day trip from Athens?

I'd look at the drive times and see what works better for you. Since it sounds like you have limited time in Athens, I would not do a day trip and instead incorporate it into your driving trip.
I read this article recently and it really made me want to incorporate an overnight next time I get to the region:
https://www.nytimes.com/2019/07/09/travel/delphi-ancient-greece-oracle.html

Its too bad the flights to Naxos will be taking off just about when you arrive. There are several transatlantic flights that all arrive between 9:30 and 10:30 so a noon flight makes sense.

My comments you will be jet lagged count on it. Drink lots of coffee at the airport. Be prepared to stop once or twice for more coffee on the way.
The drive to Nafplio is on a major highway. It is a toll road. We didn't set our GPS to choose toll roads so it tried to take us through a heavily contested urban route. Make sure you take the big highway urban driving in Greece is a nightmare especially jet lagged.

By the way we rented from ACR Athens Car Rental. They meet you at arrivals, take you to the car at arrivals go over the car (its a good idea to video the car as they do look for new dings and scrapes when you return the car.) I missed two dings on the inspection but my wife had them on her phone video. At the end of the trip you return the car to the airport departure level. We made the mistake of returning the car to the place where we picked it up and that almost cost us a missed shuttle to our hotel. We have rented from ACR three times and they are the best locally owned rental agency.

After you turn south off the National highway you will be on a narrow hilly and gently curvy road through Nemian wine country. Although you might be tempted to do a bit of sightseeing perhaps some wine tasting just keep going. by the time you get to Nafplio you will be ready to crash.
If you want to do Delphi you are going to need 4 or 5 days to get over jet lag, explore Nafplio and surrounding sites and then doing Delphi on the way back towards Athens. We planned our arrival in Delphi for late afternoon. We found a hotel on a walk up basis. You will get a discount rate if you get your hotel this way. Its early season and the hotel owners really want your business. We visited the museum to get oriented on what is in the site. You might even want to visit the lower site which has no gate and is open 24 hours a day. Next morning get to the gate for the upper site at opening. This will beat the tour bus crowds and yu will have the site virtually to your selves for about 2 hours. By then you will be at the top of the site and the crowds will be at the entrance which will give you another hour of peace. You can easily feel why the ancients called this place the center of the earth.

Perhaps yu could consider a visit to Corinth on the way back to Athens airport. It has some amazing site including Nemia, Jans favourite but also Ancient Corinth and the amazing fortress at acrocorinth.
Plan your return to the airport in time for that afternoon flight to Naxos.

Here is a preview of your trip. Have a great time.
Nafplio and Peloponnese http://www.flickr.com/photos/stanbr54/sets/72157632094108982/
Corinth area sights https://www.flickr.com/photos/stanbr54/albums/72157711755443483

Naxos Town http://www.flickr.com/photos/stanbr54/sets/72157632094558042/

Trip around Naxos

http://www.flickr.com/photos/stanbr54/sets/72157634605629689/

Naxos trip 2019 https://www.flickr.com/photos/stanbr54/albums/72157711294807761

And if you decide to drive to Nafplio make you know where to turn off the toll way. I had expected that the rental car place would give us a map but they did not. I did not have one and we took the wrong turn-and we were not even jet lagged!