Assuming you're flying from DFW, get to BOS (AA miles/Avios?) and fly Icelandair from there. It's a 5-hour economy flight, and depending on your travel dates, you can probably fly economy for about $600. The recent Icelandair promo for buying miles was remarkable because their miles were actually much more useful on Alaska Airlines for flights to Hawaii than they were for flights to Iceland. It's 50K points from the US to Iceland in economy. Unless you're cash poor, this is probably not a flight to spend miles on.

Even better, plan a trip to Europe on Icelandair and stopover in Iceland. Free stopover. Price to European cities is competitive, and the stop in Reykjavik breaks up an otherwise long flight.