My wife and I stayed at Kankaso for two nights in early April 2013.
First things first, I would recommend Kankaso without hesitation, for all the reasons laid out below. However, it is expensive (we paid £600 for two nights, 12 tatami, priovate bathroom, two breakfasts, one dinner). If you want to experience a comfortable, well-run ryokan serving superb food in a beautiful location then it is worth every penny. This is a place to really cherish your accomodation in, not one to use simply as a bed at night after exploring the area and having dinner/drinks out.
The location is perfect. It is within Nara Koen, within a hop skip and jump of Todai-ji and the big buddha and close to so many of the other beautiful temples and shrine within the park.
Our room was lovely, very spacious and comfortable, with chairs to relax in with a view of the front garden. We had private access to the large baths (I think there were not many people staying the first night we were there), plus a smaller wooden bath in our room.
The food here was spectacular. We only had dinner the first night (to save a little expense) but it was unforgettable. Certainly the most elaborate meal we had in our two weeks in Japan, it consisted of many 15 separate courses, each one beautifully crafted and very tasty. There were a lot of items that were foreign to an English couple (some of which we couldn't identify even after tasting it and asking what it was!), but everything (bar perhaps one fruit/nut-like item) was delicious. The only thing that took us by surprise is that we were offered beer or sake, which we duly accepted, which was then added to our bill. At around £150 for two people to have dinner, and given the way it was offered, we'd expected this to be included in the cost. For the record, dinner is very expensive, but it's certainly worth trying for one night of your stay - please don't miss it!
Breakfast, like dinner, consisted of many courses - fish, rice, tofu, pickles, miso, etc. It was even more of a foreign concept to have all this for breakfast, but it was tasty, it was substantial, and it set us up really well for a day of walking around the park.
Fortunately, Nara is not that large. As a result, there is not very much to see of the town outside of the beautiful park with its shrines, temples, etc. (although there is a lot within the park!) This works well as you could easily spend a whole day lazing around Kankaso - bathing first thing in the morning, taking a long, leisurely breakfast, another bath, a nap, another bath, a rest in the garden with a book, your evening meal, another bath and a rest before bed.
To reiterate, I would not hesitate to recommend this place. If you plan to relax and take it easy in Nara, go for it. If, though, you're looking purely for accomodation in between busy days out and about, there may be better budget options around.