We have flown Iceland Air several times through Keflavik on to Europe & back. As Agnes has already pointed out, the Reykjavik airport is small and connections are easy.
Just be aware that Iceland Air, while not quite a discount/"no frills" airline, is an airline with lower service standards than the majors. That having been said, on occasion I have found their First Class seats priced to be virtually the same as the majors' coach seats and have therefore tried their First Class service. I found it equivalent to domestic First Class (i.e., simply wider seats with better food and fight attendant attentiveness).
We've also done the "free stopover." Suggestions and observations:
- Reykjavik is nearly an hour away from the airport. Plan on a $100+ taxi or $35-$40 per person bus trip. However, there are a few hotels right by the Keflavik airport but the area is otherwise pretty isolated.
- You can get better tour and hotel prices by searching on your own.
- The Iceland Air tours are 50 person buses. For the same price you can get a tour in a 12-16 person mini-bus.
- We took the "Golden Circle." In all honesty, it was interesting but after living in the Rocky Mountain West there was not a lot to see (virtually no wildlife and/or greenery). The land is pretty barren. Unless you're really into isolation, a day or two is all you need.
- However, we've found that an overnight stop in Keflavic is a decent way to help with west-to-east jet lag.
Please ask if I can help any more.