We were fortunate to go to the Roman museum also. Fascinating as to the mosaics and other artifacts. It was a little gem.

Took same trip 2 years ago and stayed extra in Lucerne. Hard part in Lucerne is between lake cruise, and going up into the mountains. If you haven't been to a lot of mountains - the time would be worth it to take the whole trip, great photo op. Food is expensive. choose restaurants wisely, we enjoyed a lot of the baked flat bread with veggies, better than pizza.