I am not a great meat fan, I am not a Japanese cuisine fan and I am not a Shabu Shabu or Sukiyaki fan. However, I am aware that many of you out there like it so I might as well tell you about Mo Mo Paradise ("Mo Mo" stands for the mooing of a cow, source of the meat you will eat), which is cheap, ubiquitous and fairly good.
At Mo Mo Paradise, part of the chain which owns Fujimama and Barbacoa, the deal is simple: 1500 yen for all the Sukiyaki OR Shabu Shabu OR both you can eat for two hours. There is an all you can drink set including sake, cocktails, wine and soft drinks for 1200. Do not expect much in terms of atmosphere. As I am sure you realize, at an all-you-can-eat restaurant, that's not the attraction.
Telephone numbers
Shinjuku East Exit 3356-4129
Shinjuku 3-chome 5363-4629
Juyugaoka 5701-4129
Ikebukuro 5950-4129
Shibuya 3461-2941