Les Baux has a surprisingly good restaurant scene for a village of its size, though prices reflect the tourist trade. The best option is to eat in the village itself on a weekday, when the crowds thin, and choose carefully.
Oustau de Baumanière, just below the village, is one of the most celebrated restaurants in Provence — two Michelin stars and a long history of feeding the world's wealthy and well-connected. It's expensive in the manner of haute Provençal cuisine: beautiful produce, perfect technique, a dining room designed to feel like a film set. The terrace views over the Alpilles are extraordinary.
For something less expensive, the village's handful of bistros offer solid Provençal cooking — lamb from the Alpilles, tapenade, cheese from the hills — in historic settings. Avoid the worst tourist menus posted at the entrance; a few places still cook honestly.