First place to visit is the Quartier Saint Jean where you'll really feel the History of the capital of Gaul. Visit the Traboules (nice Renaissance passageways between the buildings with carved staircases), get lost in the labyrinth of middle age streets, visit the cathedral and enjoy the "bouchons", small restaurants with a great cuisine.
Second place is up the Croix Rousse Hill. The view over Lyon is great and you may even see the Mont Blanc if the wheather is clear.
You can also visit the Roman Arena on Fourvière Hill (use the funicular, it's fun). One of the best restaurant is just round the corner: Christian Têtedoie.
Downtown, the centre of the city is the place Bellecour. From there it's only a stroll away to go to the "Musée des Tissus et des Arts décoratifs". The museum is my favourite and the exhibition of costumes is a nice reminder of Lyon past and present reputation for silk trading.