Check Out the Monterey Kyoto Hotel
Monterey is a Japanese-owned and operated chain with somewhere around 15-20 properties. We stayed in their Kyoto property on the Karasuma-dori (the main street that runs away from the railway station); absolutely beautiful, wonderful and charming staff, and their own rooftop "onsen". The Kyoto subway had a stop about a block away. I think you can get a $150 per night rate there.
We did do a guided tour on one of our days in Kyoto, which hit the highlights in Kyoto in the morning and the highlights in Nara, about 40 minutes by road away from central Kyoto, in the afternoon. As we had been in Japan a week by this time and were pretty much worn out from all the walking we had done, doing a guided tour for one day was right for us (my wife and I are in our mid-50s).
A JR 7 day pass is worth it; we did the Green Car pass, and it turned out that the cost of the pass was only a few yen more than a single Green Car round trip from central Tokyo to Kyoto. Not only did we ride the Tokaido Shinkansen to and from Kyoto, we also went to Nikko (about 100 miles north of Tokyo and really worth a look), rode JR trains all around Tokyo, and I did the Joetsu shinkansen through the mountains up to Niigata and back, just to do it. There are plenty of on-line travel agencies that can set you up with the pass-they send you a receipt, which you take to a JR service center (there is one on the mezzanine between the arrivals exit in NRT Terminal 1 and the rail station platforms; another one is in Tokyo station), show the agent your passport, and they issue your passes right there (and make seat reservations if you want them; all Shinkansen green cars are all-reserved).
I love Japan; it is sensational. I've even printed out instructions on how to read and write the Hiragana alphabet, and even have picked up a few words (Kita is north, Higashi is east, Minami is south, and Nishi is west--how about that?). I'm sitting here looking at about Y8,500 that I had left over from my last trip--I cannot wait to go back.