I haven't eaten at the Villa Principe Leopoldo and probably would first just have lunch on the terrace if I was there on a warm and sunny day. There are exceptions but I have the feeling that hotel restaurants rarely offer the same price/performance as independant restaurants. It's likely that the spectacular view is part of the meal there but the food should be quite good as well.
There's another one Michelin star place about 5 miles outside of Lugano which I haven't tried but also comes recommended. It's called "Motto del Gallo" in the village of Taverne. And if you want to try a Grotto, here's a list of a Swiss journalist's favorite ones:
My favorite grottos by Luigi Bosia