New Orleans — 80km east, about 1 hour — is the obvious base for this region and an easy day trip in either direction; most visitors use New Orleans as their anchor and treat Donaldsonville as a stop on the River Road rather than an overnight destination, but it works both ways.
Thibodaux (40km south on Bayou Lafourche) is the main town in Cajun Lafourche Parish — the E.D. White Historic Site (home of a former US Chief Justice) is here, and the town has a genuine Cajun character without being set up for tourism.
Baton Rouge (35km north via US-61) has the striking Art Deco Louisiana State Capitol building — the tallest state capitol in the US — and the Old State Capitol, a Gothic Revival castle on the river with good exhibits on Louisiana political history. Allow half a day.