Vienne, 30 km south on the Rhône, is a Roman town with one of the best-preserved Roman temples in France (the Temple of Augustus and Livia, built in 25 BCE), a large Roman theatre, and an excellent town-centre market. Reachable in 20 minutes by TER train.
Beaujolais — the vineyard country immediately north of Lyon, accessible by car or bicycle from the city's northern suburbs — is a gentle landscape of hills, stone villages, and wine estates. The Route des Vins de Beaujolais connects the main villages. The Beaujolais Nouveau release each November (third Thursday of the month) is celebrated more enthusiastically here than anywhere else in France.
Annecy, 1 hour 40 minutes by train east of Lyon, has a mountain lake and a perfectly preserved medieval old town built over canals. Worth a full day.