Luzern is one of my favorite cities in the world, enjoy it there!
I would recommend of course:
The Chapel Bridge and the lake, but also:
Take a look at St. Leodegar, you have a very nice view from up there; the railway station is worth a look; what I definitely recommend is visiting the KKL, the culture and congress centre there. It is a magnificent building with a protruding roof. The architect wanted to include the water of the lake, nearby which it was build, into the building, so he led small canals into the building. Inside it there is the best concert hall in the world, except maybe the Golden Saloon in Vienna; and this hall from the outside looks like a ship, swimming in those canals.
At last, where to eat...
I have one recommendation for you there:
The Zunfthaus zum Pfister in the street Unter der Egg, they serve fantastic local food like fondue...
But there are of course a lot of other great restaurants
Have a nice trip!