Best things to do in Hamilton are the things just outside the actual city. The escarpment means there's some good hikes and mountain biking, particularly up toward Ancaster/Dundas. Waterfalls all over the place. Picked a shitty month for it, although it will probably be nice after a snowfall tomorrow.
Canadian Warplane Museum by the Hamilton Airport is actually pretty cool, if you're into that kind of thing. I know some people from Australia who are pilots and way into planes, and they knew about it and were dying to go. It's apparently pretty famous among aviation enthusiasts. It has one of two remaining Lancaster bombers in the world that still fly.