If you fly Icelandair, they usually do a pretty good all-inclusive stopover package. They have their own hotel (the Loftleidir) in Reykjavik, which is where the buses from the airport at Keflavik drop off their pax. They do a fantastic buffet on Sundays - all you can eat, including lots of local delicacies including reindeer and whale.
Don't forget to try out the open air hot baths (powered by the natural geothermal system) and if you get a chance, go to Geysir where you can see, yes, gesirs!
Pity you weren't staying longer than a day, because there's plenty of other very interesting places to see - Ragnarsjokull, and areas of the interior which are identical to the moon: so much so that's where Neil Armstrong and the other astronauts practiced their moon walks! Plus there's the world's oldest parliament...
The Icelanders are incredibly hospitable. Yes, it's very expensive (especially the booze) but I'm sure you'll enjoy it regardless!