Vienne is a good place for lunch, but there are more opportunities in Valence, later on.
After your walk, head back to the train station, where you'll buy a ticket to Valence unless you're really set on exploring my favorite French wine region, the Hermitage, in which case you'd get off at Tain l'Hermitage and go exploring. In any case, you'll see the legendary Crozes-Hermitage and Hermitage vineyards off to the left of you as you get near to Valence. They're on steep slopes, and signposted with the names of the famous wineries.
The first famous vineyards you'll see coming from Vienne (and some of France's oldest) are of the Côte Rôtie, the "roasted slopes." Viognier and Syrah grapes are planted here, in vineyards started by the Romans.
Then you'll pass vineyards planted in viogner--the 105 hectares of Condrieu. Chateau-Grillet comes next, the only appellation in France that consists of a single winery! Just in case you're thinking that a bottle of the white would be a treat, they usually go for well over $100.
On the right side of the train as you near Valence, you'll come across the Cornas vineyards which supplied Charlemagne with one of his favorite wines. Cornas means "burnt land," and produces a lusty red wine.
Valence has many restaurants in an attractive setting. You'll want to see the Cathedral of Saint Apollinaris, built in the 11th century. Le Musée International de la Chaussure (International Shoe Museum) contains nearly 8000 objects related to shoe making. Narrow little streets called cotes are the oldest streets in Valence; walk tall in the footsteps of visitors Rabelias and Napolean.