The Brasserie du Casino, attached to the Grand Casino complex facing the Parc des Sources, is the most atmospheric place to eat in Vichy. The room is a high-ceilinged Belle Époque brasserie with the full complement of dark wood, mirrors, and white linen, serving a menu of classic French brasserie dishes: steak, fish, charcuterie, good cheese. The food is not revelatory, but it is reliably competent, and eating in this setting — with the park visible through the windows — is a pleasure that justifies the slightly elevated prices.
The terrace in front of the brasserie, facing the Parc des Sources, is worth noting separately. On warm evenings in summer it fills with a good mix of thermal visitors, locals, and tourists, and the view across the park to the illuminated opera house is genuinely lovely. A decent wine list with good Auvergne and Loire choices.