Find apartment
Hokkaido University has dormitory (Hokushin dormitory) near campus (15-20min by bicycle).
Single room with bed and desk. You need to share toilet, shower, kitchen and living room with other students.
You can stay with comparably cheap price (less than 20,000 yen / month) and make some friends.
Unfortunately, not many rooms are available for international students.
In addition, you have to find apartment after one year staying in the dormitory.
Hokkaido University cooperation (CO-OP) owns some apartments, and also can support you to find apartment, so feel free to ask if you need any help.
Hokkaido University CO-OP has International Students Committee.
If you failed to enter the dormitory and need to find apartment after you came to Hakodate, you can stay in guest house near campus until you get proper place.