Flying to Geneva, help me with where to stay?

[Clumzy]

Found some extremely cheap flights to Geneva in the October half term and am wondering where, within good driving distance, that we can stay.
The flights are cheap because of it being shy of the start of skiing season so obviously I'm not hoping for snow.
Been to chamonix around that time of year and really enjoyed it so that's my back up plan but it's quite expensive there, whatever the season, and I was actually maybe hoping to see more of Switzerland than France.
Anyone any suggestions!?
Two adults and kids aged 6-13

Anywhere along the lake is beautiful - Lausanne to Villeneuve in particular. Not cheap though.

Otherwise Annecy?

Bern is not too far and you can go via Gstaad and Chateau d'Oex. Then on to Interlaken and Bernese Oberland - trip on train to Jungfraujoch via Wengen or Grindelwald, and possibly up Schinigge Platte (do check as it may close earlier in October after Swiss school mid term break or be weekends only).

Thank you, I will search up all of these suggestions ☺️

Montreux is lovely. It may be simpler to go by train rather than driving - the airport is very well connected.

Everywhere in Switzerland is expensive though.