Morioka is a small city, but it offers a number of good drinking options. The water in the area is clean and pure so there are a number of sake breweries. Japanese style 'Izakaya' bars are everywhere, and there are also some German style beer breweries which offer a variety of brews.
Ootaru
Oodori 15 minutes walk from the station. japanese-style eatery with asahi on tap and ¥1,500 2.5hr nomihodai all you can drink deals. try the pizza.
As with most cities in Japan, karaoke is a good drinking option, especially if you have a large group. Most places are ¥1,000 an hour, including drinks. A good place is right off Odori on the forth floor across the street from Ootaru.
'FACES' is a western-style and western-owned bar and club near the movie theaters on Eigakan Dori movie theater street. Great place to meet other English speakers!