Sep 6, 2016 - 10:49 PM
in reply to Blairp
Slowpoke covered the Lucerne/Wengen part very nicely. As far as Zermatt goes, try taking the train to Gornergrat, then walking back to Riffelalp to catch the train back to town. The view from Gornergrat is superb! You can, of course, walk all the way back, but after Riffelalp the path goes through a lot of woods and there isn't that much to see.
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For another excellent, but longer, walk, take the cable car to Schwarzsee at the base of the Matterhorn and walk back via Staffelalp and Zmutt. This walk is mostly downhill. You can shorten it a bit by catching the Furi cable car for the last leg to Zermatt.
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A couple of tips. Zermatt sits in a very narrow valley so you will need to take some form of mountain transport to get to the areas with the best views, but it is well worth the expense. If you are planning to catch a cable car/train back to town, check the time of the last service before you start. Some of them close quite early.
Watch out for mountain bikers on the trails, particularly below the treeline where the paths can be very narrow. Zermatt is very popular with riders looking for 'Extreme' runs and a lot of the time they will barely be in control. If you hear one coming, try to move off the path because they may not be able to stop or manouver around you.
Have a great time!