If museums are on your list of things to see in Aomori, then you might want to head to Nebuta Museum WARASSE. If you want to see more of the museums in Aomori, you can easily walk to Hakkodamaru Memorial Ship.
You can learn about the history of Goshogawara with a trip to Tsushimake Shinzashiki. Stroll along the seaside or visit the temples while you're in the area.