I'd say the best hike of my life was the glacier point hike in Yosemite, which was an 8-9 hour hike mostly downhill, over 3 waterfalls and tons of scenic views of Yosemite Valley.
I'm taking my wife, and we're both in good but not athletic shape. We'd likely take a train or a hikers shuttle to the top and walk down. I've lived in Georgia/Florida for 20 years, so we don't do well with high altitude ascents. Single track, not paved, and moderate difficulty, I'd say.
The two drivers are photography and the name recognition of the hike, if that makes sense. I've done about 3 hikes that are considered some of the best in the world, and hiking the perimeter of the Matterhorn has a lot of appeal.
Still, we're thinking of a mix of culture and hiking, which is why we may skip the Matterhorn area, which is south, and stick to Bern > Interlaken and Grindelwald/Murren. Bern for the culture and the rest for the sights.
The problem is that I think Zermatt has the best hiking, it's just off the beaten path. I saw this pic on Flickr.. I'd say this type of trail is about perfect (the Matterhorn is in the top left).