Toho Cinema theaters (http://www.tohotheater.jp/) are a nice venue to watch movies in Japan. A good way to enjoy yourself is to buy your tickets in advance, sample a tasty meal and relax in the comfortable red chairs.
With Toho Cinemas you can purchase tickets in advance and online. They have comfortable chairs, and a wide range of snacks/meals. Unlike the typical American offerings, they have unique items such as the "Tsukune Rice Burger" (http://www.tohotheater.jp/news/conse/food.html)
They also have "discount" days where tickets are cheaper than usual. Every Wednesday is ladies day, and general admission tickets for females are only 1,000 yen.