There are two main drinking districts in Hakodate, Daimon, which is close to the station, and GoryÅkaku, in particular Hon-Cho. Foreigners seem to be more catered to in the GoryÅkaku area.
Bagus
A surfer-style bar open 'til morning.
Ramaru ã©ã¡ã¼ã«
honcho 2-3 Alpha Building
9pm - 4 am
Small drinking place 2nd floor. "Nomi-ho Dai" All you can drink for 1 1/2 hours-3000Yen. Look for a "Blue Ship's Anchor" on the sign next to the Boss coffee machine. This street has many bars so it is a little confuzing to find. But if you find it- it's well worth a chat with Osho-san. the owner.