There are three BBQ areas at CERN: Prevessin, Meyrin and LHC PA2. You can book one of these areas through this link: https://indico.cern.ch/rooms/book

Alternatively, there is a park near Plage de Vengeron, on the lake in Chambesy. Grilling/barbecue facilities are available, but you must bring your own coal and lighters. This can be reached by taking the train number R 11057 from the train station in Geneva (Gare Cornavin) in direction of Coppet, the stop is Chambesy. From there you must walk 15 minutes to arrive at Plage de Vengeron (Route de Lausanne 284, 1292 Chambésy).

Spacious grassy park with a stony beach and barbecue grills are also available in Versoix (Plage de Port-Choiseul). This can be reached by taking the train number R 11057 from the train station in Geneva (Gare Cornavin) in direction of Coppet, the stop is Pont Céard. From there you must walk 10 minutes to arrive at Plage de Port-Choiseul.

Information about Geneva beaches can be found here. By clicking on different beaches you shall find out whether is is possible to BBQ there.