Two active 72-year-olds, experienced travelers planning another Swiss holiday. We really enjoyed a trip a few years ago, St. Moritz then down to Tirano and Lake Garda. Thinking about a base near Lake Geneva for a 7-10 day trip in 2024. We don't like moving about and don't like cities, so were thinking a base (resort? hotel?) near Lake Geneva where we have several day trip options and can enjoy a different region of Switzerland. Appears we could easily visit Italy and France from this area...plenty of mountains and peaks...plus the lake. This seems to fit our style. Running from train to train and hotel to hotel every couple of days does not appeal to us. We also may have the option of buying a week-long RCI or Interval timeshare in that general area, or alternately finding a decent resort or other property. Our previous trip was in early September and seemed to be a great time of year to visit. Generally, am I on the right track here, looking for some feedback...

Lake Geneva is actually Lac Leman. Check out Montreux. It feels like a small town. I stayed there many times and made day trips to Geneva, Lausanne (Olympic Museum), Gruyeres/Broc (cheese and chocolate), high peak/glacier area (Glacier 3000), the Lavaux area with terraced vineyards down to the lake, Aosta (Italy), Chamonix (France) and Evian-les-Bains (France). Montreux is close to Chateau de Chillon . The band Queen had a studio in Montreux. Freddy Mercury recorded his last song there. It is located in the Montreux Casino and is free to visit.

For day trips by public transport, Chexbres, Vevey, Montreux, Glion and Aigle might be good bases..
Check airbnb and booking.com
if you don't mind to spend some time in order to get down by local trains to the main railway stations, you may also check Blonay, Chernex, Caux, Leysin, Villars, Gryon, Chesieres......

But be aware that it takes time to go from Montreux to Italy by public transport:
Montreux - Domodossola: 1 1/2 - 2 hrs
Montreux - Stresa/Lake Maggiore: 2 - 3 hrs
Montreux - Courmayeur: 3 1/2 - 4 1/2 hrs
Montreux - Aosta: 2 3/4 hrs, only once daily
Montreux - Zermatt - Breuil/Cervinia 4 1/2 hrs

I also heartily recommend Montreux or Vevey.

I agree!

BarbAnn's recommendation is good. I also like Montreux. It feels like a smaller place than it is. After the castle there isn't really a lot to see in the city itself but walking the waterfront is sublime and there's a casino if you're interested. It's a great place to relax and is very central for some good rail connections.

Chamonix and Zermatt are both under three hours by train from Montreux, faster with a car. The Golden Pass train goes north from Montreux to Interlaken. Hard to go wrong.