Four preliminaries:
I never refer to guides or ratings, and this will only be my personal selection, so forget about Michelin, Gault&Millau, etc.
The city in France with the densest ratio of restaurants per capita is not Lyon but Bordeaux.
There is no gastronomical capital in France, and fortunately so — every city and region has wonders to offer. But it is true that Lyon is a unique and beautiful place for gastronomy.
According to the Lyonnais tradition, a bouchon is a place where the total price tag for a meal is below 35 euros. Now some places may call themselves “bouchons” and charge more, and they can be perfectly good, but they’re not technically bouchons. Restaurants that serve traditional Lyonnais food, yes they are.
Le Bouchon des Filles answers the description, as does Le Café du Peintre or Chez les Garçons.
Brasserie Georges is a magnificent place, and though it doesn’t exactly deliver the very best food (honorable at least), for its atmosphere and setting, it is not to be missed.
On the upper shelf, Paul Bocuse at L’Auberge du Pont de Collonges had deeply disappointed me years ago, and due to special circumstances I went again a year ago, in April. It was one of the best meals I ever had in France. The contrast was such that I told the maître d’ about it, in few words: “Years ago, the last time I was here, it was no good. Now it’s splendid.” He said: “You’re absolutely right, the quality had sunk very low at the time you’re mentioning. We tried harder and now here we are.”
Other places I like are Daniel et Denise (three locations), which never disappoints, I like the Créqui location; shopping for food at Le Garde-Manger (farm products from the Monts du Lyonnais); Le Bouchon Sully; Le Bouchon Léa; Notre Maison; a visit to Les Halles Paul Bocuse is a must. Chez Georges; Café du Jura.
Actually the whole region is fascinating, foodwise. Going East to the Bresse, I recommend L’Ancienne Auberge 1900, attached to the Georges Blanc two-star restaurant. Everything is perfect there.
And it’s worth going to Bourg-en-Bresse for the fantastic Brasserie Le Français, in the Brasserie Georges style but with better food.