Local and international cuisine are pretty good, traditional food in Kyoto has as main ingredients fish and seafood, typical food is the sushi among others are udon chiri, sukiyaki and yudofu, some sushi restaurants in Kyoto are:

Fukusuke
37 Nishitakagi-cho, Shimogamo, Sakyo-ku
Tel. 075-781-8274

Yagurazushi Shimaya
East of Minami-za, Shijo, Higashiyama-ku
Tel. 075-561-1556

Honke Jubei
Nawate-dori Shinbashi agaru, Higashiyama-ku
Tel. 075-561-2698

Tamaya Kamogawa-ten
30-19 Asatuyugahara-cho, Kamigamo, Kita-ku
Tel. 075-723-0353

Musashi (Kaiten-zushi style)
Kawaramachi-sanjo
Tel. 075-222-0634

International cuisine in Kyoto is present with a great variety of restaurants, Thai, Italian, American and many others, so you'll feel like in home if you don't like Kyoto local food you can choose any other:

Le Bellecour
Cuisine: french
59 Tanaka Satonomae-cho, Kyoto, 26 Japan
Tel. +81 075 711 7643

Ashokav Cuisine: indian
Kikusui Building, 3rd floor, Teramachi Dori.
Tel. 075/241-1318

Chorakukan
Cuisine: western
In the southwest corner of Maruyama Park, Eastern Kyoto
Tel. 075/561-0001

Misoguigawa
Cuisine: french
Sanjo-sagaru, Pontocho, Central Kyoto
Tel. 075/221-2270

The Kitchen Salvatore Cuomo
Cuisine: italian
10th floor, Isetan department store, Above Kyoto Station
Tel. 075/365-7765

Tohkasaikan
Cuisine: chinese
Nishizume, Shijo Ohashi. On Shijo Dori
Tel. 075/221-1147

Zappa
Cuisine: indonesian
Higashi-iru Takoyakushi, Kawaramachi, Central Kyoto
Tel. 075/225-4437

King & I
Cuisine: thailand
Kawaramachi dori
Tel. 075 256 5632