There are various items to take care of when you are leaving Japan and the list varies from person-to-person (for instance, single vs family case). In general, following points need to be considered:

• return books borrowed from library and clear all the procedure at the university related to leaving the university.
• if you live in university dormitory, inform the I-House office about your moving out date.
• if you live in an apartment, inform your landlord and/or real estate agent at least one month before your scheduled moving date and complete the designated procedures such as paying final rent, cleaning and disposing all items that you purchased after moving in the apartment (including big items such as bed, refrigerator, etc.). Do not remove items that were present when you moved in (such as air-conditioners, etc.). It is to be noted that disposal of some big items is not free and requires completing applicable procedures in advance. Check with the applicable garbage and recycling policy of the area you live in. Finally, the security deposit that you paid when you moved in will be returned to you after deducting expenses related to cleaning, repairs, etc.
• provide a moving-out notification to the ward office at least 2 weeks before your departure date.
• cancel your enrolment to national health insurance at the ward office and return the insurance card. Additionally, cancel any other insurance that you might have enrolled during your stay in Japan.
• cancel your contract with telephone, TV, and internet service provider (fixed phone, cell phone, internet, cable TV, etc.). Clear the pending payment for these services including service-termination charges, if applicable.
• contact each of the service utility companies (gas, water, and electricity) at least a couple of days ahead of your scheduled departure date to cancel the service and clear the pending payment for these services.
• withdraw all money from your bank and close the bank account. 
• settle your credit card bills (if you use one). If you are a holder of university co-op credit card, note that the card will expire upon your graduation. If you would like to continue using the credit-card, contact the credit card issuer to change the card type from student to regular type.
• if you paid into the National Pension Plan, complete the procedure for withdrawing and for receiving the lump-sum withdrawal payment.
• return your resident card to an immigration inspector at the port of departure.