The postcard view of Lucerne ("Luzern" in German) almost always includes this triad: Mt. Pilatus (2,132m/7000ft), the 14th-century Kapellbrücke Bridge, and its Wasserturm ('Water Tower').
The "Golden Round Trip" offered to tourists is, well, touristy, but you MUST do it--from the foothills on the city's edge, you take a series of gondola cablecars up to the summit of Pilatus for 360-degree Alpine views, then the world's steepest cog railway down the other side of the mountain to the edge of the lake, and finally a leisurely boat ride back to Lucerne. It's impossibly, almost ridiculously scenic. (Almost ridiculously expensive, too...but worth the cost.)
End the day with a beer by the bridge as the skies over the Alps turn golden...