Despite spending a lot of time in Kobe, I don't know much about Osaka I'm afraid. Kyoto however.....
I've heard good things about Okamoto Sensei in Kyoto
As for off the beaten track tourism, I recommend Saga nr Arishiyama on the Western edge of Kyoto. Tenryuji at Arashiyama is one of my favourite all time temples and there are some lovely walks through the bamboo forest of Saga, with some nice shops hidden away.
Not so off the beaten track, you of course have Kiyomizudera, Sanjusangendo, Ryoanji, Kinkakuji, all well worth a visit if you haven't been before.
When are you going? I'll be in Japan from 30th this month to 16th April, will be based in Kobe but will visit Kyoto during the trip.