Vianden has a handful of restaurants along the Grand-Rue and near the river, mostly serving Luxembourgish and Ardennes-style food: smoked pork, game in season, trout from local rivers, and the jambon d'Ardenne that appears on menus across the region. The tourist season keeps a small number of places open, but outside summer and weekends, options thin out quickly.
The castle itself has a small cafe on the grounds. For a proper meal, the restaurants on the Grand-Rue are your best option — simple food, reasonable prices, and a view of the castle walls if you get the right table.