Konnichi wa, Donna-chan. La Professoressa recommends the following:
Omen Restaurant near the Silver Pavilion in northeastern Kyoto (in a large traditionally styled building just south of the tourist bus drop-off for the Silver Pavilion). Traditional Japanese cuisine specializing in seasonal preparations and "one-dish" (ippin ryoori) selections. Food is fresh with emphasis on non-processed ingredients. Lunch and dinner. Closed Thursday. Phone: 075-771-8994.
Minokichi Restaurant, in the lower level of the Kyoto New Hankyu Hotel, just across the street from the main entrance to Kyoto Station. This restuarant has traditional Kyoto food at a moderate price. Cozy, but nice.
Nakamura-ya, in an alley just north east of the main intersection at Kyoto University (at Hyakumanben). This little shop specializes in yakisoba and okonomiyaki, which are cooked on a iron griddle at your table.
For all variety of edibles made with green tea (ocha)--soba noodles, cake, ice cream, etc.--look for the Hayashiya Chaya. The new and enlarged restaurant overlooks the Kamo River from an upper floor (just across the street from a huge Starbucks). Enter 1 and 1/2 blocks west of the river on Sanjo, take the elevator to the fourth floor.
For an interesting, comparatively new spot, try the Somushi, a Korean tea shop (tea, coffee, and a few things to eat). Located about a block west of the Starbucks on Karasuma a few bocks south of Oikedori.
Some other suggestions: Meigetsuen, in the heart of the shopping district near the intersection of Shijo and Yanagibamba. Also: Yamazaki near Royanji, or Sakon near Ninnaji.
Two other possibilities: the Fujita Hotel and Le Relais Okasaki for French food.
Dewa mata.