The most obvious day trip from Buenos Aires is to Tigre and the Paraná Delta — about an hour north by suburban train, then by lancha into the delta channels. The town of Tigre has a pleasant waterfront and the Tigre Art Museum; the delta beyond is a different world entirely.
Colonia del Sacramento in Uruguay is accessible by high-speed ferry in about an hour. The old town is a UNESCO site: a well-preserved 18th-century Portuguese colonial settlement with cobbled streets, crumbling walls, and a lighthouse. There is a single daily round trip that allows a comfortable day visit; a Uruguayan tourist visa is not required for most nationalities.
Closer to the city, the Pampas begin immediately to the west and southwest — flat cattle country that stretches to the Andes. Several estancias (working cattle ranches) near the towns of San Antonio de Areco (3 hours by bus) offer day visits that include a barbecue lunch, horse riding, and folk music. San Antonio de Areco itself is an unusually well-preserved 19th-century market town and worth seeing for its own sake.