United Airlines and Air Canada have Phoenix PHX to Reykjavik KEF, Iceland tickets throughout summer months June to September for $429 round trip.
There were tickets as low as $374 round trip yesterday on Momondo.com, but I no longer find those low fares at time of publishing.
Air Canada $428.58 round trip ticket
Phoenix PHX – Toronto YYZ – Reykjavik KEF – Montreal YUL – Chicago ORD – Phoenix PHX
United Airlines $428.58 round trip ticket
Phoenix PHX – Chicago ORD – Montreal YUL – Reykjavik KEF – Toronto YYZ – Chicago ORD – Phoenix PHX