Burlington is unusually well-placed for day trips. Toronto and its full menu of museums, restaurants and waterfront sit an hour east by car or GO train. Hamilton is fifteen minutes south across the Skyway — visit the Art Gallery of Hamilton, Dundurn Castle, and the city's chain of waterfall hikes off the Bruce Trail. Niagara-on-the-Lake (40 minutes south along the QEW) is the standard wine-region and Shaw Festival stop. Niagara Falls itself is a further 30 minutes beyond.
For something different, the Crawford Lake Conservation Area in the escarpment behind Burlington has a reconstructed 15th-century Iroquoian longhouse village; the McMichael Canadian Art Collection in Kleinburg is an hour and a quarter north.