The convent of Our Lady of Akita located on a mountain about a 20min bus ride from Akita city. Kakunodate - a small town located 45mins by bullet train from Akita.
It has beautiful old samurai houses which can be explored. These samurai house are better than the ones in Kyoto! Natural onsens are also located very close to Akita city. Akita has wonderful fresh seafood - try whale meat from this city. Whale meat is not easily found throughout Japan and this is one of the cities in Japan other than the north that has beautifully fresh whalemest/horse meat and sashimi.