Which Swiss cities offer the best mix of culture, food, and nature?

I'm pretty sure I'd avoid the cities

"Best" is, I believe, in the eye of the beholder. FWIW, I think Geneva and Zurich are both underrated. Of smaller cities, Bern and Basel have much to offer. The Green Guide to Switzerland provides excellent coverage -- you might consult it.

Big fan of Montreux. Proximity to mountain attractions, scenic lakes and paddlewheel steamers, France, Italy, many diverse things to do, moderate temperatures, transport hub, less crowded.

Zurich’s got the best mix IMO, but yeah it’s expensive as hell. Bern feels more chill and compact, but still pretty. Lucerne’s more postcard-y. Depends on what vibe you’re after.

I should have included Luzerne in my list! Note, though, that it does get a lot of tourists during high season -- perhaps a few too many.

Oh, and Lausanne!

Museums: Basel
Theatres, Opera house, concerts: Zurich
Food: top restraurants in any bigger city (and around), but at some small places like Yverdon, Gstaad, Zermatt, Verbier, Andermatt, Bad Ragaz, Arosa, Upper Engadine, Ascona, Lugano too.
Nature: all Swiss cities have tramway or citybus lines into the nature, with tons of hiking trails.
Funiculars or cableways to viewpoints from:
Geneva (Saleve),
Lausanne-Montreux (Rochers de Naye, Pleiades)
Neuchatel (Chaumont)
Biel/Bienne (Macolin)
Solothurn (Weisssenstein)
Lucerne (Pilatus)
Zurich (Uetliberg)
Locarno (Cardada)
Lugano (Mone Bre, Monte San Salvatore, Monte Generoso)