I'm going to be staying at the Kaisu Hostel and want to know if there are any restaurants I should try in the area?
I need to walk a bit, but I think that there are many stores cheaper around Akasaka Mitsuke station.
There are also many cheap stores in the two streets on the east side of Hitotsugi street.
Also around Akasaka Station there are cheap chain stores such as McDonald's, saizeriya, Burger King, Pronto, Doutor Coffee, Matsuya etc.
Get Akasaka up on Google maps then search restaurants. You will get lots of results, with cost and cuisine identified, most with photos.
You won't starve or go broke.
But since we aren't you, we don't know what you may like.
There are all kinds of Japanese, Korean, other international restaurants/bars including convenient store for box meals between and around Akasak and Akasaka Mitsuke subway stations along the narrow streets, in the alleys and don't forget to look up the 2nd floors of buildings.