Don't know what you like, but here are a few things to do.
St Georges. Beaches Tobacco Bay most popular, St Catherines nice beach with facilities. Achilles Bay (100 yards from St Catherines), more private beach.
Horse drawn Carriage ride, glass bottom boat ride. Tour Ft St Catherines. See town crier conduct a "dunking" in town square at noon. Shops and galleries. Golf.
Hamilton. Beaches like Horseshoe Bay many others. Shopping, horsedrawn carraige rides. Tour Cathedral (go to bookstore to ask about climbing to top). Aquarium, botanical gardens, take bus to Crystal Caves. Book a snorkelling tour. Best independent tour run by Jessie James. Golf, deep sea fishing. Tour government buildings. Ferry ride around harbor or to Dockyard area.
Dockyard area. Shopping, snorkel park, dolphin encounter , museum.
Look into multiple day bus passes for getting around.
One night a week there is a festival/parade in Hamilton.
Look for Michael Douglas and Catherine Zeta Jones as well as Mayor Bloomberg from NYC. All maintain residences.