In reply to stu84:
The campsite in Zermatt is right next to the railway line so from early morning to late evening there is a lot of noise from this, there sometimes seems to be a lot of freight shunting in the early morning as well. It’s also very small and only suitable for small backpacking type tents.
Better sites are available lower down the valley but not ideal for catching early cable cars.
Re huts, the cheapest hut in the vicinity of the Breithorn is the Rossi e Volanti bivouac hut which is free . It has mattresses and blankets but no cooking facilities so take a stove. It is quite high, 3,750m so not ideal until you are a bit acclimatised and no running water, only snowmelt so take enough fuel and be careful where you collect snow to melt as it also has no toilet so people “go” nearby.
You can walk to it from the Kleine Matterhorn cable car by traversing “round the back” of the Breithorn, you could do the ordinary route on the Breithorn en-route or use the hut as a base from which to start the Breithorn traverse the next day.
You can also climb Pollux and Castor easily from there. Lyskamm is a bit further but doable.
If you fancy a grand traverse you could go from this hut via some/all of these peaks to the Balmenhorn bivi hut and on to the peaks of Monta Rosa the next day though it would be a long way back so better approached from Italy unless you descend to Zermatt from Monta Rosa.
The Balmenhorn hut has blankets and a stove with gas and pans, plates, cutlery etc. It too has no running water but it does have a toilet (which is something to behold) and at nearly 4,200m you really do want to be well acclimatised before stopping there.
I believe there are some other huts in the vicinity that you can pay for but I have no experience of them