7 nights itinerary suggestion with elderly parents

Lucerne is quite walkable - although the streets are a little uneven if I remember correctly. The incline to the top of - oh darn, I've forgotten the name but it is the highest peak on the lake is a must do. A boat ride on the lake is also a very memorable afternoon trip - take the long trip. We loved Lucerne. We stayed at Hotel de Alpes - a wonderful location and ask for a room with a view.
We were only there 2 nights but really loved it.

Murren -- you can just stare at the mountains, or take the lift up to the top of Schilthorn and walk around the level deck area. We did this last September with our elderly (70+) selves. Stopped at the intermediate transfer point (Brig) on the way up for about a half hour to make sure we had no altitude reactions.

We just got off a Holland America transatlantic cruise where most passengers were very old. Many were very mobility challenged and really didn't have any business traveling any longer.
My hat's off to you taking the responsibility of traveling with parents.
But let me warn you about a situation my mother got into. My sister had a place in Aspen, Colorado and she took my mother there for a week. Mom had a very weak heart and was coming off a cold. She immediately started having breathing problems as fluid was building up around her heart. Within a day, she was admitted to the hospital where she spent a week in ICU.
Come to find out, Aspen Hospital has a revolving door for elderly patients coming through there that are incapable of handling the thin air of high elevations--and is one of the best hospitals anywhere for such problems.
In our case, Mom was flown home on a private jet and went straight into a major hospital where she had open heart surgery. We were close to losing her, but she came back and lived another 10 years.
I hope your parents are just mobility challenged and don't have heart issues because going to Switzerland or any place of high elevation can be a prescription for serious troubles.

Thank you pumpkin5 for making me feel assured with my Lucerne choice!

Laura - will there be enough to do in Murren for me and my parents for 3 nights? Is it quite walkable with stores and cafes? Is it a straightforward train ride from Lucerne to Murren? I also heard Lauterbrunnen is pretty centrally located but not sure how it compares with Murren.

David, thank you for sharing such a personal story. I'll definitely keep that in mind for future. My parents (actually more just my mom) are only mobility challenged, no heart disease. In fact, they respond even better than I did when we traveled to high altitude places.

elenaning, Yes, Luzern (local spelling) is a good choice. Old town, plenty of cafés and the like with sit down opportunities. The local mountain is called Pilatus. The other two nearby mountains also with transport to the top are Rigi and Titlis. Titlis is the highest of the three and has a permanent snow cap. The most spectacular but may be a bit too challenging.
Zürich airport to Luzern is easy. Two trains per hour (one direct, one involving a change, both take ~1h15). I recommend waiting for the direct train.

As regards Mürren, it is a small village which is not reachable by road, train and cable car only. Its attraction is the beautiful views. Do not expect much facilities. If you are not into hiking, it is a good place to "chill out" and recharge your batteries.

Geography and transport: This is a three-dimensional area. See the "panorama map" here: http://berneroberlandtaxi.ch/images/map_2015.jpg (red=train, black=cable car, yellow=bus)
Luzern to Interlaken (between the two lakes at the bottom of the map) is a direct train, over the scenic Brünig pass. Then change at "Interlaken Ost" onto a second train to Lauterbrunnen (end of the road). From here you take a cable car UP the side of the valley, then a train along the side of the mountain to Mürren. Five-star spectacular. Each method of transport waits for the previous one, and it runs every 30 minutes, so if you want to wait, no problem.
There are lots of videos on YouTube, for example this one: https://www.youtube.com/watch?v=F1NdWipvTCo

I suggest you do some Google image searches for Lauterbrunnen and Mürren.

Thank you, Chris F!