Have some Zunda-Mochi! It's a mochi topped with mashed edamame paste and looks green. There is also Zunda shake which is very tasty.
Take a day trip to Matsuhima Bay. Matsushima Bay is very beautiful and seafood there is so fresh and nice. Oyster is famous local food there. There are also temples such as Zuigan-Ji and Entsuin. Zuigan-Ji is surrounded by forests and beautiful. Entsuin has beautiful Japanese garden.