Palégrié on Rue du Palais Grillé ... it is a stones throw from the Cordeliers subway stop. Make a reservation whether you want to go for lunch or dinner.
The restaurant has two employees, a husband and wife. The husband is the chef and the wife handles the front of house. The menu changes daily based on what the chef thinks looks the best at the Quai Saint-Antoine market (located about two blocks away along the Saône river). He will come to your table and ask you what sort of foods you like and dislike, if you have any allergies, and go back to the kitchen and decide what he wants to cook for you. When I was there I had multiple locals tell me that while Palégrié is not traditional Lyonnais food, it was there favorite place to eat in the entire city. I went for lunch one day and was blown away. I unfortunately could not make it in for dinner because my time in Lyon had run out.

The Quai market is also a great place to grab lunch. Get a baguette, a hunk of cheese, and some fruits and veggies and sit on the bank of the river with a bottle of wine.

For traditional Lyonnais food, you should go to a bouchon. Dont mess with any of the places in the old part of town that claim to be bouchons. Most of them are tourist traps.
Cafe des Federations is a fantastic bouchon. It was one of the best meals I have ever had. Make a reservation one night and arrive with an empty stomach. Get multiple pots ("poes") of their house red and white wines. I think each pot is like 6 euro and has about 3 glasses of wine. You pay a set price for the meal and just choose your entree. Everything else is set. To start they bring out lyonnais salad, lentils and charcuterie, then whatever entree you decided on (try the Quenelle here), then whatever dessert they are serving that night and you end with a cheeseplate. You really shouldn't visit Lyon without eating here.

Bocuse's Le Sud is also an amazing restaurant. It is more of a nice atmosphere and white table cloth place than Federations. Just whatever fish they have on the menu. The technique at all of his restaurants is superb.

Daniel et Denise is a great place to grab lunch. They do a very reasonably priced two or three course menu and every entree comes with some of the best potatoes and mac and cheese you could imagine.

Hope this helps. Lyon is one of my favorite places in the world. I am extremely jealous that you are going. If you hit up any of these spots take some pictures and share them in here.