I live in Anchorage, AK. My girlfriend and I want to go to Reykjavik next spring/summer. What is my best option for using airline rewards points? I have a wide variety of points in UR, MR, AA, AS, etc... I am aware of the seasonal flights from ANC to RKV, but wanted to know other options.

I can fly out of anywhere in the US if need be. What US cities have direct flights into Iceland? What alliance would be the best? I am looking for Economy tickets.