Try Sushi at 21, a classy restaurant on the Marktplatz. They also do a great selection of teas.
Alternatively, go to the Karren panorama restaurant, which perches on the side of a mountain above town. They serve mainly good typically Austrian cuisine! You can see it from everywhere in the city. The view over the Rhine Valley and Lake Constance is stunning night and day and it's often sunny up there when it's foggy down below. They do a very good value cable car and meal combination ticket on weekday lunchtimes. To get there take the number 5 bus from the station to the Karrenseilbahn cable car.
