Feb 29, 2016 - 1:29 PM
Well, you can't visit the Matterhorn itself but there are various viewing points. I like Gornergrat very much; you'll be passing the Riffelsee on the train and you can easily hike to it (in summer). Klein Matterhorn is higher and closer to the mountain, but you will have a side view there, not the view like you see it on the postcards. Sunnegga is another option.
Cable cars and mountain trains are pretty expensive, so I'd recommend the Swiss Transfer Ticket Combi. It includes the train rides from Zurich airport to Zermatt and Zermatt back to Zurich. Also you will get a 50% discount on further rides. Please see the link in my previous post for where to buy, but be sure to select the correct rail product on that page, and click "Show results". If you plan to stay in Zurich for the night after your return trip you will need an additional ticket to the airport the next day as the Transfer Ticket will be expired.