In reply to Mike-P1607:
I'd say that the iconic mountains are the Weisshorn and the Dent Blanche but maybe I'm biased. The Weisshorn is very obvious from the Barrhorn - I'd recommend a traverse from St Luc to St Niklaus with a night at the Turtmannhütte so doing the Barrhorn on the second day with an early start.
For spectacular scenery it's hard to beat the view from the Cabane du Mountet - you can do it as a day trip from Zinal but it's worth staying at the hut for the sunrise on the Dent Blanche.
Two nice routes a wee bit to the west are the traverse of Le Luisin going up Les Fleuriers (SE ridge) and down the west ridge and the traverse of Le Catogne (W-E) from Champex-Lac. Both give good views over the Mont Blanc massif and you can see most of the Valais peaks.
Switzerland isn't that expensive as long as you avoid restaurants and hotels! Beer in huts is expensive as it has to be flown in by helicopter but I'm still amazed that it costs less than in central Geneva and Zurich where it's delivered by road.