There are cheap places in Japan. For example Gyudon, beef rice bowl, chain stores like Yoshinoya and Matsuya offers a medium sized rice bowl in less than 500 yen. Also, a Tendon, Tempura rice bowl, chain stores called Tenya, offers a basic tempura rice bowl in about 500 yen. Hanamaru Udon offers a bowl of udon in like 300 yen. They are all located in major downtown areas.
Also, old-looking Izakayas or standing type Izakayas tend to offer food and drinks in low prices. However, those places tend to not have English menu or English speaking staffs.