I'd agree with wideman on the whole objectives of ryokan stays. It's the whole experience of it, very relaxing and to unwind. That said, I would probably get more out of a ryokan stay in a resort area as opposed to one in a bustling city like Tokyo, where you tend to be on the move all the time.

My wife and I went to ryokans in Beppu and Yufuin, about 35 mins apart in Oita Prefecture, Kyushu, to partake of the hot springs baths there. Enjoyed it a lot. I'd recommend staying two nights if you can, but if the budget is tight, just stay for one.