Île de la Cité shares the Seine River with its upstream neighbor, Île Saint-Louis, right in the middle of Paris's city center. The westernmost end of the island is mostly residential with a small park at the tip, while the eastern end gives visitors the best view of the flying buttresses of Notre-Dame Cathedral. The Palais de Justice is also housed on the island, which has the Sainte-Chapelle inside, a tiny jewel box of almost kaleidoscopic color thanks to its wonderful stained glass.
Archaeologists found evidence of habitation on this island by the Romans, as early as the first century BC. But the early 17th century was when the island came into its own, after the construction of the Pont Neuf that spans the river and intersects with the western end.
The Île de la Cité is actually the geographical center of Paris, and as such it's easily reachable. From the Left Bank of the Seine, the M4 Saint-Michel stop is the closest. The Right Bank's stop is Châtelet, with the M1, M4, M7, M11 and M14 all stopping there. And on the island itself, the M4's Cité stop is the only Metro station.