The following universities need TOEFL, not many. University of Tokyo (IELTS is also acceptable), Kyoto University, Nagoya University, Tohoku University, Yokohama National University (TOEFL is also acceptable), Kyushu University, Hokkaido University, tokyo institute of technology, and Hayata University (TOEFL is not required for science and engineering, but for business).
Private universities such as Jinggu University, Chiba University, Telecommunication University and Yamanashi University are among the best. There's not much left.
The above universities need TOEFL scores, but universities that do not need TOEFL scores but have English tests are recommended: Saitama University and osaka city university.
Many universities require toeic.