Wolfenbüttel's restaurant scene is modest but serviceable. The town centre has a handful of German and Italian restaurants clustered around the Stadtmarkt and the streets leading to the castle. Lunch crowds mostly consist of locals and library researchers, which is a reliable indicator of quality.
For traditional German cooking, look for the family-run Gaststätten near the old town that serve regional Lower Saxony dishes: roast pork, Grünkohl with Pinkel (a cured sausage) in winter, and hearty soups. The market square has cafes suitable for a light lunch or coffee after the library or castle.