The distinctive red building houses exhibits about the Nebuta, including several floats, if you're unable to make it during festival season.
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青森ベイブリッジ Aomori Bei Buridji
This bridge spans a short harbor inlet near Aomori Station and the former ferry port.
八甲田丸
The ferry which connected Hokkaido and Aomori prior to the building of the Seikan Submarine Tunnel is now a somewhat run down museum, but worth checking out if you're interested in regional history, trains, or boats. The rear part of the deck of the ferry serves as a beer garden on summer nights.
アスパム
A large triangular building that can be easily spotted from the train station or the bridge, this is the tourism center for all of Aomori prefecture. It includes a movie about the prefecture (Japanese only) and an observation deck with views of the harbor and city (extra charge).
まちなか温泉 machinaka onsen
If you're tired, weary, and want a bath without going all the way to Asamushi Onsen, you can enjoy a hot spring bath just a few minutes walk from Aomori Station. The small bath outside is nice.
善知鳥神社
There are nice gardens and ponds tucked away behind the main shrine. There's also a "power spot" -- it's said if you wash your coins in a certain fountain there, you'll be free from money troubles.
青森県立美術館
Exhibits about the natural and cultural history of Aomori prefecture.