Thanks for everybody's tips.
I stayed at Eden au Lac using the Expedia special weekend rate of 280 francs. This was a very nice hotel with great service.
Kronenhalle was nearby, but if you want to eat there on a Saturday evening, you need advance reservations. I didn't eat ther, but the dinner servings looked adequate for 4 people. I didn't try their "best in the world" chocolate mousse, but the mouse at the hotel was definitely better than any US made chocolate mousse.
Brunen is a very scenic town. I stayed at the Seehotel Waldstatterhof. The room next to mine was the Winston Churchill room, whe he spent his honeymoon. Beuatiful view of the lake and the mountains every morning.