There are also cable cars that go up to adjacent peaks.
Surprisingly we found the food was not much more expensive (if at all) at the mountain top restaurants and you can't beat the view!
Zermatt and all the surrounding peaks are connected by a myriad of paths, something like 250 miles. It is about a 3 hour downhill hike to go from here back to Zermatt. Later in our stay we hiked part of the way down (downhills are really hard on my ankle, I'd much rather be going uphill).