You can sit at the counter at a lot of kaiseki restaurants. One I go to a lot is Gion Tanimoto in Kyoto (075-551-8011). Just make sure your concierge makes a reservation for you at the counter. I don't think, like many other kaiseki restaurants -- or restaurants in Kyoto for that matter, that it takes cards, but it's quite reasonable (Y8000 a head for dinner), so as long as you go easy on the sake, you don't need to carry arround more than $250 cash.