Léon de Lyon is not a bistro. It is seriously the BEST restaurant in the city. I would highly recommend it, but it is a Michelin 2-star, and can be pricy. You will definitely need a reservation there.
I can't lie... Chef Jean-Paul Lacombe is a very good friend of mine., so I may be prejudiced, but most folks I've recommended any of his places to have thought them wonderful.
He also owns a whole bunch of casual bistros in the area. I've enjoyed both of those on the rue Mercier, Bistro du Lyon, where I celebrated New Years in 2005 and Bistrot du Vin. These are less formal and you well may be able to walk in there, especially at lunch. As I'm writing this, I can still taste a fabulous Pumpkin Soup with candied chestnuts.
As well. George Blanc, who has a 3-star in Vonnas up the road from Lyon, has a bistro called Le Splendid in Lyon where the food is great and the prices reasonable. Also notable is Comptoir du Boeuf in Old Lyon, the bistro owned by Philippe Chavent who owns La tour Rose.
A great place for lunch is Giraudet on the Place Bellecour where they serve some of the best quenelles anywhere in France.