New York JFK and Newark EWR to Geneva or Zurich, Switzerland is as low as $322 round trip for departures March to June. It is also possible to book a near free stopover in Iceland.
I was unable to get Icelandair to price a stopover on a JFK-Geneva round trip, but it does work with online travel agencies when the return airport is changed from JFK to EWR.
Icelandair New York JFK – Reykjavik KEF – Geneva GVA – KEF – JFK
Expedia ticket with Iceland stopover
Icelandair Newark EWR – Reykjavik KEF (3 night stopover) – Geneva GVA – KEF – JFK