If you're here for cherry blossom season, a trip to Hirosaki Castle (about an hour from the port) is a must. The surrounding park is home to more than 2,500 cherry trees and walking through the blossoms is an unforgettable experience. There are great photo ops, including cherry trees next to the restored castle, with snow-topped Mount Iwaki in the background. The nearby Tsugaruhan Neputa Mura complex houses huge floats from Hirosaki's festival, as well as craftspeople doing traditional work.
If you stay in Aomori, Nebuta Museum Wa Rasse displays that city's gigantic festival floats. Nearby, check out A-Factory for all things apple, including cider. There's also a lively downtown shopping area.