Kagari, the Michelin starred restaurant, must be the most famous one. I tried to go there once but there were too long lines and I gave up.
I visited to Ginza Oborozuki the other day, it was pretty nice.
They had a thin noodles tsukemen, which is unusual, and I liked it much!
Also near Oborozuki, there is a place called Hashigo.
This place specializes in "Tantan-men", which is a spicy sesame ramen topped with ground meat flavored with miso.
Hashigo has larger seatings comparing to Oborozuki.
A shop named Kazami was recently made, but an unusual soup with sake, but it is very tasty and recommended.
Other famous stores are gathered here.