Québec City is well placed for day trips into the surrounding region. The three most useful are covered as POIs on the Things to Do page: Montmorency Falls (15 minutes east), Île d'Orléans (20 minutes east), and Mont-Sainte-Anne (45 minutes east).
Baie-Saint-Paul (90 minutes northeast on Route 138) is an attractive art town in the Charlevoix region, with a strong gallery scene and the beginning of the spectacular scenery that unfolds as you drive up the north shore of the St. Lawrence. The Charlevoix coast — dramatic cliffs, whales in the estuary, and a distinct local culture — is worth several days of exploration if time allows.
Grosse Île (50 km east, accessible by ferry from Berthier-sur-Mer) was the Irish quarantine station for immigrants arriving in Canada in the 19th century; the Memorial to the Irish Famine of 1847-48, when thousands died here, is one of the most moving historical sites in Canada.