Onsen Town with Easy Access to Narita Airport

Ifll be in Japan in August and will have two days at the end of my trip before my flight out from Narita. I want to stay in a traditional ryokan in an onsen town, ideally in a picturesque, rural setting. But the key is that I need to be able to easily get from there to Narita airport by 8:30am on the day I depart. Ifm happy to take a train, a bus or even a taxi, but I just need to make sure I can reliably get to the airport in time, and without too much stress. Any recommendations? Thanks!

I would recommend Atami. It has plenty of traditional ryokan, good onsen, beautiful scenery, and a much easier connection to Narita Airport than many of Japan's more remote onsen towns.
Hakone would be my second choice, but Atami is probably the best balance between a traditional onsen experience and a stress-free departure day.....
Furuya Ryokan
Atami Sekitei
Watei Kazekomichi
Atami Korakuen Hotel

Arriving by 8:30 am at Narita airport severely limits your choices. Atami wouldnft be reasonable. Per Google Maps youfd need to take a train 4:30 am to arrive on time.

I would suggest a nice onsen / ryokan for one night somewhere in the Kanto area and the art hotel Narita for your last night:
https://iconia.co.jp/hotel-art-hotel-narita-chiba

It has a real onsen with several pools and offers airport shuttle.

Alternatively there are some other ryokan options (if the ryokan rather than the onsen experience is the main attraction for you) close to Narita. Eg you could look into Ryokan in Narita city itself. On the main approach to Naritasan temple there are several ryokans. and Narita city itself is nice enough.

A lot depends on how you define "easy access". The trains are pretty reliable. Plus does it need to be at a famous resort type area, or just anywhere?
BTW maybe google was having a major hiccup or something, but Atami to Narita doesn't have to take 4 hours at all. You can take the bullet train to Shinagawa or Tokyo Station quickly. Both Jorudan and Ekispert give the same info - the fastest way takes 2 hours. Go to Tokyo Stn, take the Yamanote Line to Ueno, and then take the Keisei Skyliner to Narita. Not cheap and a bit of a hassle, but it is possible with a 6:25 AM departure. The big wrinkle I would add though is if you have luggage and you are going on a weekday, the morning train rush hour to get to Ueno might be a big headache. There is another option though, to take the bullet train to Shinagawa and then the Narita Express at 7:30 - but you'd arrive at about 8:35, if that extra few minutes is critical for you. Rushing to catch a train to the airport is not on my list of favorite things though, to be honest.

@Ken is right. My Google Maps had a hickup. However youfd still need to take a very early train and have little leeway to miss a connectionc and youfd need to navigate Tokyo station in rush hour to get on the Yamanote line on the connection I found that gets you before 8:30 to the airport. To me that sounds like a lot of stress, thus proposing at least for the last night something much closer to Narita.

Narita town is actually quite nice. Ifd venture to say itfs nicer than Atami as a city. But those are individual tastes.