The closest airport is Hakodate Airport (HKD). The airport does not have international direct flights from/to European and US countries. You need transit at the hub airports: Narita International Airport (NRT) or Tokyo International Airport (HND).
Using HND is the easiest way to arrive HKD. At HND, please transit your airplane to a domestic flight which is going to HKD. The airport has several domestic flights (10 flights per day) to HKD. Generally, the flight takes 1.5 hours.
NRT is the largest international airport in Japan, then most passengers arrive at NRT. However, there is no domestic flight between NRT and HKD. Therefore, you need to move to HND by public transportation (bus) and take a domestic flight to HKD. The bus takes near 2 hours, and the bus costs 3,100 yen. You can get more detail information about the bus from their website [link]. At HND, you can take an airplane to HKD.