Geneva

Check with whatever hotel you will be staying in to see if they have "guest cards" which will give free local public transport.

This website should help you:
https://www.myswitzerland.com/en-us/destinations/holiday-destinations-in-switzerland/geneva.html

If you'll contact the tourist information office (Tourismus) they'll answer your questions. The contact info is on the myswitzerland.com website above.

Hotels and "holiday apartments" usually give you a free public transportation pass, upon request, for their city and nearby.

If you arrive by train, there's a handy Migros store in the station where you can buy some food before you find your hotel. Also, you should be able to pick up bus maps at the RR info center. Both are one level down the steps from the trains.

If you arrive at the airport, after you get your luggage at the carousel, look to your right as you exit that room and you should see a free bus ticket machine that will give you about an hour of free bus rides. (It was there last time I looked.) The #10 bus goes from the airport into town with a stop at the Cornavin train station.
Every hotel/hostel in Geneva should give you a free bus day pass. Ask about it.

Stuff to check out:
The free bus tix also cover 2 water taxis that cross the lake/river.

Free bikes to rent ( geneveroule.ch )

Red Cross Museum

Calvin's church (climb the bell tower)

Wed. and Sat. there is a flea market at Plain Palais

At any store, check out Rivella, a soft drink not sold outside Switz.

Go to the cathedral in the middle of the old city. They have excavated underneath it down to the 1st century and you can walk through all of it...Roman mosaic floors, wells, burials, etc. Really interesting. The shops in this part of town are fantastic as well - antiquarian bookstores, antique shops, art galleries, etc.
If you are into science you can visit CERN - you have to make a reservation but it is well worth the effort. It's really incredible what they are doing there.
Obviously you can walk along the waterfront which is lovely.
Take the train to Vevey, Lausanne, or Montreux to see the Chateau Chillon. All three are on the north side of Lake Geneva.

Thank you for the info!