Many foreign visitors include Lucerne on their itinerary. What they often do not realise is that the lake they see in Lucerne is very big and stretches down to Brunnen and then changes its name to the Urnersee and then extends to Flüelen. If there is time do not miss the chance to use the ferries and get maybe a dayticket to travel these boats. You can get off at any of the stops, and maybe walk to the next station.
As you travel down the Urnersee the scenery is more rugged, try getting off at Treib and take the small train up to Seelisberg and maybe walk up the road there and have a look at the beautiful converted hotel which housed the global headquarters of the Transendental Meditation Movement of the Maharisi Mahesh Yogi from 1968 until 1992. Close by is the Rütli Meadow where the Swiss Confederacy was signed.
If you do not wish to take a day trip go from Lucerne to Vitznau and go on the train up Mount Rigi, or to Burgenstock. All these places offer spectacular scenery both in summer and in winter. The trips may be a little on the expensive side but worth it. Have a look for offers and look at www.lakelucerne.ch to see the offers.
I have personally travelled to all these places over the last fifteen years, never am I disappointed.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.