Have a Japanese friend help you check out possible travel deals that are available at the time you need.
Being on a student visa, the OP is ineligible for a JR Pass, but JR typically offers a number of shuuyuuken, which provide roundtrip travel from one's home base to a specific region (Kansai would be a good bet, with Kyoto, Nara, Osaka, Kobe, and dozens of less known sights) and unlimited travel on JR lines within the designated region.
Another option would be to shell out the money for a Shinkansen roundtrip to the Kansai area and then buy a Surutto Kansai debit card to facilitate transportation on Kansai's extensive network of privately owned (and cheaper) train, bus, and subway lines.