Café de Ville is a traditional cafe in the Lucerne old town with views of the lake. They are a popular spot for morning coffee with pastries and afternoon tea with dessert. This would be a great place to warm up after doing a walking tour of the city.
The interior is quite formal and feels more suited to their evening dining on hearty Swiss classics. But service is friendly and I always feel welcome even if I'm just ordering a cappuccino while I wait for friends.