My wife and I will be taking a Switzerland tour in 2 weeks. On the tour there is a free day in Lugano. Question I have is it worth taking a boat trip to Gandria or Marcote. In Luzern the tour is giving us 2 free nights after the tour ends and looking for places to visit. Considering Mt Pilatus or Mt Rigi, or taking a ride on the lake to some small towns. I am not interested in the museums around town.
For your free day in Luzern, you can do a nice loop trip to Rigi, using the lake boat to Vitznau, up to the top by rack railway, back down to Rigi Kaltbad, change to the cablecar down to Wegggis, and back to Luzern by boat. there are easy to moderate hiking oppurtunities at both Rigi kaltbad oand Rigi Kulm (the top), with gorgeous views over the lake.
The above suggestion enables you to combine Mountain and lake. Good recommendation. The other day you can use for wandering around the center of Lucerne- Lion Monument, Kappel Bridge, old town center, Mirror maze and Glacier garden. Relaxed lunch outdoors eating something Swiss.