A ryokan is not really a 1:1 substitute for a hotel. A ryokan, especially a high-end ryokan as LapLap has booked, is best suited for relaxation and unwinding. It is not nearly as well suited as a place to touch down, quickly wash your face, rush out and explore the city, stop back for 10 minutes, then go run out again. There's nothing at all wrong with the latter way to visit a city, it's just that I wouldn't choose a ryokan if that were my plan.

That said, I'd definitely go for 2 nights. In many ryokans, you are asked to check in after 3pm and check out in mid- or late morning, which doesn't give much opportunity to peel back many layers of the onion. And while you're likely to be served an elaborate (kaiseki) dinner the first night, the ryokan will likely give you the option for a different type of dinner on subsequent nights. Or, as dhammer experienced, you may be able to opt out of dinner with some appropriate price adjustment.

My guess is that 10 years from now, you'll remember the ryokan experience about 20 times more clearly and happily than the hotel experience. (Not that the hotel would be bad -- but it would simply be one among many.) Go for 2 nights, and be sure to tell us about it when you get back.