If you want to get close to Tokyo, Saitama city would be the closest. Then there is Ashikaga, Tochigi with the oldest university in Japan. And of course where I live, Gunma has universities in Takasaki and Maebashi.
If you are accepted to a university, you will probably be eligible for dorm housing, which would make the expense of living in a place like Tokyo a bit easier to handle.
However, if you REALLY want to learn Japanese, try for a homestay. Nothing like total immersion to get you going!