Of course, national universities are better than private universities.
Good private universities such as:
Waseda University, Keio University, sophia university, Meiji University, Tokyo Rikkyo University.
Kyodo University in Kyoto, Ritsumeikan University
Osaka Kansai University, etc.
It is best to choose a national university, not only because it is good, but also because the tuition fee of a national university is nearly half cheaper than that of a private university.
The better private university is Tokyo Home Economics University, followed by Heyang Women's University and Sugino Fashion University.
I hope it helps you.
Feel free to consult if you have any questions.