Schongau's eating options are modest but reliable. The town has a handful of traditional Bavarian restaurants around the Marktplatz and along the main streets of the Altstadt, serving the usual southern German repertoire of roast pork, dumplings, and Schnitzel. Weekend lunches can be busy with locals; midweek the restaurants are quiet. Most places close one or two days a week, so it's worth checking before you go.
There's a weekly market on the Marktplatz where local farmers sell bread, cheese, and seasonal produce — good for assembling a picnic before heading out to the Lech valley.