I think we need a little more info about what you wish to study and any other goals you have. Also, what are you studying? Japanese, Japanese culture, both? I studied at Akita International University outside Akita City. There is almost nothing near campus but with an amazing library and computer lab both opened 24 hours, various support services, and open and supportive faculty, I would recommend it for a year or less program. Keep in mind the snow is a little rough there though!
That would really depend on what you will be studying. Like for instance, if you will study fashion and photography, then universities in the Shibuya area would be great.
Generally, universities in Tokyo are good, but are also very expensive. But for sure, it will give you a great experience, anyway.