My view is that Lugano is not much different from Switzerland's other lakeside towns, and there is no snowcapped mountain as backdrop.
For Gotthard Pass make sure you take the mountain road and not the tunnel. There are a couple other passes near Andermatt which are quite beautiful as well.
Stein am Rhein is a very colorful and beautiful town. Schaffhaussen is right next to Rhine falls. You may take a brief visit.
If you go as far as St Gallen, you can visit Liechtenstein and Appenzell. Apenzell is a nice little town and the town center is off limit to vehicles.