とんかつ
It was Genjiro Kida, second-generation owner of Rengatei in Ginza, who developed the tonkatsu recipe in 1899. There was no such word as tonkatsu at that time though; they called it pork cutlet (and they still do there.)
Rengatei also was the first to serve the standard side, shredded cabbage in 1904.
Rengatei (est. 1895)
3-5-16 Ginza, Chuo-ku, Tokyo 104-0061 Japan
phone: +81(3)3561-3882
The word tonkatsu was coined circa 1930. There are a few theories about the origin though, such as Ohroji in Shinjuku and Rakuten in Ueno.
Asakusa/Ueno was the shopping/entertainment/nightlife district of Tokyo back when tonkatsu was getting popular among people; many old tonkatsu restaurants in the area are still around, including the famous three:
Ponta (est. 1905)
3-23-3 Ueno, Taito-ku, Tokyo 110-0005 Japan
phone: +81(3)3831-2351
[thick strip cutlet is one of specialties]
Horaiya (est. 1914)
3-28-5 Ueno, Taito-ku, Tokyo 110-0005 Japan
phone: +81(3)3831-5783
[tenderloin tonkatsu, fried in lard]
Futaba
2-8-11 Ueno, Taito-ku, Tokyo 110-0005 Japan
phone: +81(3)3831-6483
[trimmed loin. no kids allowed]
Recent trend is, very light texture of overly-tenderized meat, the signature recipe of Isen in Yushima and its branches/spawnouts as well as the imitators.
Isen (est. 1930)
3-40-3 Yushima, Bunkyo-ku, Tokyo 113-0034 Japan
phone: +81(3)3834-2901
Maisen (est. 1965)
4-8-5 Jingumae, Shibuya-ku, Tokyo 150-0001 Japan
phone: +81(3)3470-0071
Tonkatsu Restaurant League