Icelandair and WOW are both low-cost airlines based in Iceland. Icelandair offers free checked bags, WOW charges for checked bags (and even for overweight carry-ons).
Here is a low cost deal from New York to London, with a multi-day stopover in Reykjavik, Iceland.
http://www.theflightdeal.com/2016/04/11/visit-2-cities-icelandair-403-new-york-newark-to-london-england-and-reykjavik-iceland-roundtrip-including-all-taxes/
This fare is available for September and October travel.