by walkingpoles » Tue May 22, 2018 9:44 am
Local here. The really big hills (3500m) are too far away, and september is the end of the season. Smaller hills abound, though, you'll enjoy it.
I don't know about camping. It shouldn't be a problem far off civilisation. Swiss people will usually stay in a SAC-hut, where there will be proper food and beds (hauling up a big back for 2km of heights is an issue). Most huts will already close at some time in september though.
Daytrips from Zurich often go the the Canton of Glarus (check out Vorderer Glärnisch) or St. Gallen and Grisons (check out Calanda for two of my favourite non-technical day hikes. Calanda can also be done as a two day hike).
Be aware of bad weather. While you can get away in Scotland in miserable conditions as long as you know what you're doing, the alps are less benign. Especially lightning strikes are not uncommon.