Chez Vrony is in the tiny village of Findeln, a short walk or quick ski from the top of the Sonnega funicular.

It's one of several small restaurants in the village, but seems the most professionally run, with an interesting and (by Swiss standards) adventurous menu and welcoming staff.  It belongs to a long-time Zermatt family (Pirmin Zurbriggen, the famous ski racer, is the brother in law of the owner) and is decorated with pictures of the family over the generations. 

The view is magnificent - direct to the Matterhorn - and the many balcony and terrace seats face full sun all afternoon.  Prices are, well, Swiss, but not at all extortionate compared to the competition. 

They've recently started accepting credit cards, and booking is definitely necessary in anything like high season.  They have a website with more details at:  http://www.chezvrony.ch/.