The strangest one is the Haskell Free Library and Opera House in Quebec and Vermont that sits on the Canada-U.S. Border. There’s a line in the middle of a room which is the border between the two counties.
Closer to home for me is Campobello Island in New Brunswick where I live. To get there from Canada, we have to take two ferries – one from mainland New Brunswick to Deer Island, and then a second ferry to Campobello Island. But the island is connected to the mainland in Maine by a bridge, so you can drive there but you have to go through the US to get there.