Two rivers cut the city into strips, and the strip you sleep on decides how much walking and how much climbing you do.
Presqu'île — between the rivers, and the default
The peninsula from Place des Terreaux down to Bellecour holds the shops, Les Halles Paul Bocuse and most of the mid-range hotels, with metro at both ends. Flat, central and priced for it; the streets off Place des Terreaux are loud at weekends.
Vieux Lyon — Renaissance streets, small rooms
The Saint-Jean quarter under Fourvière hill is the oldest fabric in the city and the part the coaches come for, so rooms are small and old and the streets are busy from mid-morning. Metro D and the F2 funicular share a station, which makes the hill painless.
Pentes de la Croix-Rousse — cheaper, steeper
The old silk-weavers' slopes above the Presqu'île: tall workshop buildings, student bars and lower prices than the flat city below. You pay in stairs, and there is no metro station halfway up the slope.
Part-Dieu and La Guillotière — for the train, not the view
East of the Rhône around the main TGV station: business hotels, hostels and the cheapest beds in the city, about fifteen minutes from the centre on the metro. Useful if you are arriving late or leaving early, unremarkable otherwise.