Explore shops, treat yourself to some Swiss chocolate or a watch walking down Bahnhofstrasse (Station Street). Visit the Matterhorn Museum. Explore the Old Village in Hinterdorf (rear village) and its preserved traditional-style buildings.
There are many different hikes in the Zermatt region for varying levels. Two of the highest recommended are: Easy Difficulty - Riffelsee Lake should take about an hour and is convenient from Riffelalp and the Gornergrat Bahn. Follow Riffelseeweg signs from either the Rotenboden station (5-10 minutes) or from Riffelalp. Medium Difficulty - 5 Lakes Walk takes around 5 hours round trip (longer for stops and photo-ops). Goes past 5 mountain lakes and allows for swimming in 2 of them. The hike starts at Blauherd mountain station. Take the underground funicular to Sunnegga then switch to a gondola to get to Blauherd.