This is a fun place to gather in the evening: a collection of 25 food vendors in an old-style marketplace, with outdoor seats (when it's not freezing). You can take your pick from ramen, donburi (rice bowl) dishes and typical izakaya fare. Most places have picture menus; figure about ¥2000 per person.
Walk straight out of JR Hakodate Station and turn left at the first traffic light.