For proximity to CERN and ease of access to public transport, staying Swiss-side is probably advisable.
Here are some of the local options most convenient for CERN. All are not far (whether by foot or a short bus-ride) from the No. 18 tram which connects direct to CERN.
Meyrin
Hotel NH Geneva Airport
https://www.nh-hotels.com/hotel/nh-geneva-airport
Auberge des Vergers
Geneva Airport
IBIS Geneve Aeroport
https://all.accor.com/hotel/3535/index.en.shtml
Hotel Holiday Inn Express Geneva Airport
https://www.expressgeneva.com/en/index.php
Of course, more options can be found online at https://www.myswitzerland.com/en/accommodations/hotel-search/-/geneva/
Public Transport (Geneva)
TPG is the public transport network operator in the Geneva region, for buses, trams and boat-taxis on the lake.
CERN is most commonly accessed by the No. 18 tram, which runs from the city centre.