Day trips with mobility issues

We stayed in Geneva and it would be an excellent base as you can easily spend two days in town. Annency is an easy day trip and easy to walk around in for another day. You can also ferry to some of the neighboring lakeside towns such as Yvoire.

Chamonix is walkable as well and there are many trips by tramway that are doable however, you may find some of the stairs to overlooks harder to negotiate.

Ironically, I have been paying attention to mobility issues as a good friend with Parkinsons is similarly challenged but still wants to travel. All of the places have consistent paved surfaces with few hills to climb.

A friend of mine asked,why can't you stay in one town a few days and another for a few days.
My answer was that if we had one large bag,and 2 small between us,at our age,and condition,it would be difficult to ,even withwheels,transport all the pieces through the train station to the train.
And also,train storage could be an issue as well

Zurich is eminently walkable, but the quaint old town IS cobblestoned. There is a guided walking tour of the highlights daily from the TI.

You could take a boat on Lake Zurich to any nearby town, alight/explore, and return by train.
Rapperswil is a marina town at the southern end of Lake Zurich, just 30 minutes away, and quite pretty. Einsideln (of Black Madonna fame and home to Kirsch-a specialty cherry liquor) is also a contender, although it's a bit of a walk to get from the train station to the monastery.

Stein am Rhein is also quite pretty, with the painted houses, and castle looming above.
Again, the train station is a scenic walk just outside the town center.

Interlaken is nearly 3 hours from Zurich one-way, though the views of Jungfrau, Moench and Eiger are memorable.

Montreux train station sits up ABOVE the lakeside promenade. But there are buses (and cabs?) available. The lakeside promenade is wide, paved, flat, and lined with flowers and benches. The views across Lake Geneva, to the French Alps are gorgeous! Chateau Chillon is about 1 and 1/4 mile away, but buses can whisk you there and back.
Know that Montreux is 3 1/2 hours one way by train.
Check sample train travel times at sbb.ch/en.

But Montreux is only just over 1 hour from Geneva.
And Gruyere is less than 2 hours with a couple of train changes.

Are you choosing Geneva or Zürich because then you can arrive, take a taxi and settle into your hotel? If you were to choose something more central then you could easily go to for more areas of Switzerland as 2 hour and under day trips. Somewhere like Bern if you want a more city feel, or Thun if you are okay with something a little smaller, but mostly flat, easy to get around and a great location for day trips.

Both Geneva and Zürich are hilly and full of busy young people going about their workday which results in more crowded sidewalks on which people are moving quickly and purposefully - at least that is my experience whenever there, and especially so when compared with someplace smaller like Thun.

Do look at SBB.ch for travel times, as suggested by wynoka54, and when you do you will see that Interlaken is actually just over 2 hours one way from Zürich Flughafen and under 2 hours from Zürich HB (not 3 hours) and Montreux can be reached in 2h 33min from Zürich HB (not 3.5hrs)

If you were to search for the city least suitable to pick as a base to visit Switzerland you would arrive at Geneva. It is as far from the most of the sights as you can get.

My suggestion would be to pick Luzern as a base. I would also skip Vaduz (which is probably the most underwhelming destination in Europe).

I thought I had mentioned the reason.guess another senior moment.
To be honest,I,not my wife,overpass on vacations. I have my reasons.
Fom what i have heard about European trains,you cannot check luggage,so it would be difficult for the 2 of us to transport 2 wheeled carryons,and a larger wheeled suitcase,through a terminal,to the train, and then carry it on board .
It is just easier for us ,at this stage,to stay in a city,with a direct flight
15 to 20 years ago,would have been different.
In the 1960s,the great Mick Jagger sang what a drag it is getting old "

i would never recommend a large suitcase and two rolling carryons for a train trip regardless of age. Not for me thanks, and I am very pro train (but still drive my car to Continental Europe.

I asked my wife (I threw an arbitrary lentgh of stay out there)
And said,if we went to Europe, could we get away with just the 2 carry on.
She did not give a verbal answer at first.
Just "the looks that meant sh doubted it.
Then said,I don't want to take away from sightseeing to do laundry.
And as I stated above,for some reasons,I pack more than her.
For example,we recently went on an 11 day cruise, had 2 large bags and 2 carryons

So, with the advice already given, its seems most of us here would favor staying in Zurich over Geneva.
Bern is a lovely old town 1:30-1:56 away with arcaded double level shops, beautiful old, ornamented fountains every block or so, Einstein history, bears, a bendy river (Aar).

I still like the small lakeside town of Rapperswil, known for its roses, Capuchin monastery, polish castle and children's zoo.
30 minutes south by train.

Every train schedule I see gives travel time to Montreux as 3:25-3:40 (oneway) from Zurich Hauptbahnhof (main town train station), but the views to the French Alps are crazy beautiful.
Only you can decide if sitting on a train for 7 hours in one day is worth it.
Much closer is the lakeside promenade in the small city of Zug (40 mins one way). A small old town and its amazing cherry Torte cake are well known (Kirschtorte).
Schaffhausen and the Rheinfalls are just 1 hour away, and can be taken as a day tour.

Not sure what your wishes/sightseeing goals are on your daytrips--mountains and lifts? lakeside? castles? history? flowers?
IF you have not already visited Luzern, I would recommend it as a priority!

Combination of history(especially medieval) and views of alps

Which the north shore of Lac Leman (aka Lake Geneva) has.

Thought of Geneva and montreaux and annecy

@margincall1947, yes, taking everything into account regarding the kind of travel and holiday you want, Geneva does seem like it is the right fit for you. As Sam has been pointing out, it seems to offer just what you are looking for!

@wynoka54, something is wrong with the method you are using to see train times. Be sure you are looking at a time that makes sense in Switzerland - perhaps you are looking at current schedules when it is actually nighttime here. I am not sure what else it could be. Check these specific departure times to see what I mean:

Zürich - Bern 56 min (9:02, 9:32, 10:02, 10:32, etc). I know several people who make this one hour commute for work.

Zürich - Montreux
9:02 = 2h 33min,
9:04 = 2h 46 min,
9:32 = 2h 37 min

Carrie posted a great link showing how to use the SBB app

https://community.ricksteves.com/travel-forum/switzerland/fyi-sbb-app-and-ticket-types-explained

If you end up going to Montreux, across the street from the train station is an escalator that will take you down to the lakefront. It might look like the escalator is not working, because it doesn’t continually run. But, if you approach it, it will start to run.

One of my favorite walks in Switzerland is walking along the lake with all the flowers and views of the mountains.

My last trip to Switzerland involved 5 different hotels. So, I understand not wanting to deal with luggage on the trains. It can be stressful.