Ok, the situation is this...
Ryokan in Tokyo are for tourists. Real ryokan are not in Tokyo as people who live here tend to get away from the place for a change of scenery.
I personally would not stay in a Tokyo Ryokan. Tokyo is a major city and does not naturally lend to a ryokan experience.
What I would suggest though is to look for a place near Narita. There are many ryokan in that area and you would be well placed to get to the airport with little trouble.
Some of the ryokan even have a shuttle service to the airport.
I say ditch Tokyo after your hotel stay is up and head on out to Chiba, try Motono village or Kozaki town for starters. You will see a different side of Japan by doing this and also be close to the airport. Note: Sorry if you are using a different airpot
