Lucerne is one of the most scenic places in Switzerland. You could walk along the Aare river and just smell the fresh air from the mountains. Stroll around the cobbled stone of the Old quarter where the 4 main squares are found. This will brighten your day in an instant. If museums interest you, Wagner museum and the Picasso Gallery is found right around the corner.
Another place to see is Mt. Pilatus. This is where they say Pontius Pilate was buried. Ride the Pilatus Railway towards this mountain. This is also the highest railway in the world.