Sacré-Cœur sits atop Montmartre's highest point, its Romano-Byzantine white travertine domes visible from much of Paris. Construction began in 1876 as an act of national penance after France's defeat in the Franco-Prussian War, and the basilica was consecrated in 1919 after decades of work. The architecture is earnest rather than elegant, but the hilltop position is unbeatable.
The views from the steps are superb and completely free — better, some would argue, than the view from inside the dome. Come early morning before the tourist masses arrive and Montmartre actually feels like the bohemian village it once was.
The neighbourhood below is worth exploring at length. Place du Tertre is tourist-trampled but still atmospheric. Nearby streets — rue Lepic, rue des Abbesses — have good cafes, bakeries, and wine shops, and the vineyard on rue des Saules is the last working vineyard within Paris. Métro: Anvers, then walk up or take the funicular.