If you're arriving at Perrache train station than I recommend this walk as a good introduction to Lyon: walk across Place Carnot (beware of drug users, prostitutes and pickpockets who plague this square from 9pm onwards), follow Rue Victor Hugo to its end stopping to look at the top name boutiques and shops.
At the end of Rue Victor Hugo is Place Bellecour. From Place Bellecour turn left to cross the Saone river and enter the Fourvière district via the Pont Bonaparte. Go straight across Quai Fulchiron and enter Place St Jean and explore old Lyon at your own pace.
Walk out of Perrache train station and keep going straight
Updates
If you're arriving at Perrache train station (or worse still, the bus station), then escaping at maximum speed should be your priority. As an alternative to walking the length of the busy shopping street rue Victor Hugo, turn left when reaching Place Ampère, passing the Basilique St-Martin-d'Ainay, nestled in the quiet, bourgeois Ainay district. Just at the end of the street to the north-west, pass under the arch on Voute d'Ainay to reach the Saône quayside, and stroll along to the footbridge affording a pleasant view across to St Georges church and the Fourvière hillside. Cross the bridge and begin your discovery of Vieux Lyon via the St Georges district at its southern end. Note that Fourvière is the name for the second cathedral and its surroundings on top of the hill, not the area below, which is simply Vieux Lyon.
Is this your business?