3 nights per stop is an excellent idea. It gives you a decent buffer against losing all your time at a given location to bad weather. And September usually delivers the best weather conditions for hiking.
With two weeks, you could probably make a decent clockwise trip around the country from Zürich to Basel. Let me start off with a recommendation for a much less well known location not terribly far from Zürich- Flumserberg. It isn't one distinct town or village, but a number of hamlets spread across the lowert slopes of a mountain (but still fairly high altitude). Flumserber isn't a major international resort, more of a rustic weekend getaway for Zürich residents. So, it has enough tourist infrasturcture to make visiting easy, but not so much that it overwhelms the community. It has two major advantages. One,
you can drive your car up the mountain, and if needed, use it to go between the various hamlets. Two, it's great location for easy hikes that still provide a knock-out view. If you take the ski lift up to the top of the mountain, there's several kilometers of mostly flat or gently sloping hiking trails (if you decide against the lift, though, a pretty vigorous hike up the mountain awaits you). I can highly recommend Hotel Cafrida.
People on this website seem to like Luzern, but I've only driven through.
Definately plan a stop in Zermatt. Yes, the town is very touristy, but one look at the magnificent Matterhorn and you won't care. And once you ascend above the valley, the high jagged peaks of the Pennine Alps towering above you are a sight like no other. But in my opinion, the hiking here is anything but easy.
Most of my experience in the Berner Oberland is in the winter, so I'll let others comment on the general difficulty level of hiking here. The hikes appear very popular with Mr. Steves' readers, and knowing that their general age demographic isn't exactly young adrenaline junkies, I can't imagine his recommended hikes are particularly stressful.
I've only driven by Montreaux, but that view from the lakeside looking towards the Alps is simply breath-taking.