Another pleasant place to visit is Sunnegga. You can either hike here from Zermatt or take the "Alpine Metro." Sunnegga, or "sun-trap" in the local dialect, affords sweeping views of the valley and the Matterhorn. And guess what? There's a restaurant here, too. You can sit on the patio and stare at the Matterhorn to your heart's content.
Before you head right on up to the Rothorn though have a look at the view of the Matterhorn from the restaurant terrace at Sunnegga - it almost seems close enough to touch from here. Perhaps closer than at Rothorn but of course you do not see as much of the other peaks. So have a coffee and enjoy the view before you head for the connecting gondolas.
Sunnegga offers probably the best view of the Matterhorn. You can reach Sunnegga easily by foot. The whole area around Sunnegga is actually perfect for walking.