For a cheap and easy way to see the highlights of Yamagata City, jump on a ¥100 Utoria bus, and grab an all-day pass for ¥300. You can jump on and off the bus, which runs every ten minutes, as often as you want.
There's plenty to see and do along the route, from museums and galleries to cafes and restaurants, so do it all once, then ride around a few times just to enjoy the view.