Lyon sits between the Saône (slower, prettier, west of Vieux Lyon) and the Rhône (bigger, east of Presqu'île).
Vieux Lyon is on the Saône (west bank). Part-Dieu and Tête d'Or are on the Rhône (east bank). Presqu'île is the peninsula between.
The rivers meet at Confluence, the modernist new neighborhood with the Musée des Confluences (worth a visit).