My personal favorites were both on Waseda dori near the intersection with Meiji dori between Waseda University and the Takadanobaba Yamanote station. Kokuran is my favorite, it's right by the Indian embassy. It's one of those pre-eating ticket purchase places...favorite meal was karamen (spicy noodles) tonkotsu ramen, and ALWAYS buy kaidama (2nds on noodles) for around 900 yen total.
2nd was Ippudo, still on Waseda dori, but nearer to the University. This place had the most customizable ramen I've ever had...5 degrees of noodle hardness, and about 5 or 6 different condiments on the table. Fantastic food, relatively cheap prices...I remember paying less than 1000.
I heard Kokuran was #3 in Tokyo according to some list. What is it about Japanese and best of lists?