Do you mean Minato-ku? A ku is an administrative district, and Minato-Ku is one of the central Tokyo ones. Wherever you are in there you won’t be very far from the Yamanote Line, which you get you pretty much anywhere in central Tokyo. There will be no shortage of places to eat - I once read a (possibly madeup) stat that Tokyo has more restaurants than the whole of Western Europe.
A few places I used to like (with the caveat that it’s a fair few years since I’ve been to any of them). I’m a vegetarian, so a lot of traditional fish based Japanese food was out for me but I never went hungry. I did once go to a very high end very traditional vegetarian place where the food was fantastic, but I literally spent the whole evening terrified that every single move or gesture I was making was some appalling etiquette faux pas.
Nirvanam in Kamiyacho, which does fantastic Indian food - http://www.nirvanam.jp/home
Nataraj in Ginza is also good for Indian food -
http://www.nataraj.co.jp/en/ginza/E_GinzaTop.shtml
Junkadelic - Mexican food in Nakameguro - http://www.junkadelic.jp/
Pure Cafe - vegan cafe in Aoyama http://www.pure-cafe.com/
Mominoki House is a good vegetarian place in Harajuku http://www.mominoki-house.net/essence/concept_en.html
Gonpachi in Azabu -more of a tourist trail thing than a destination restaurant, this is where the big fight scene in the first Kill Bill was filmed. http://www.gonpachi.jp/nishiazabu/?lang=en
There are lots of chain / family restaurants around, which are mostly competent but uninspiring. There are also several “English” pubs, all of which are worth avoiding. The brilliant thing about almost every restaurant in Tokyo is that you just get up when you’re finished and pay at a till near the door and leave. No faffing about with catching waiters’ eyes or pantomining signing bills.
