I was there for a few days over July 4. A great place and I definitely want to return.
Icelandair will allow (or did) for a stayover of up to 72 hours going between North America and Europe, and I think you can take a whale watching excursion from Keflavik.
I spent 2 full days (well, 1.5...didn't head out until lunchtime one day) in Reykjavik, a full day the first day and a half day the second. After about an hour or so the second day I was about ready to stab myself until I wandered into the weekend market where you can buy hakarl! It wasn't that bad...didn't need any schnaps...bought a Diet Coke and actually didn't take a drink for several minutes. I tried puffin a little later and it was salty...not sure if that was how it always is or due to the hakarl. I also spent 2 days on excursions from the city. While you're on the tour company's time table, you get to see some things that otherwise might be very expensive to see ($10/gal gas).
If/when you go I suggest a whale watching excursion, going to visit Gulfoss (a huge waterfall), Al(the character that looks like a P and b combined)ing...where the North American and Eurasian tectonic plates meet, as well as visiting the southern coast and the town of Vik, where you can see black volcanic sandy beaches. And stop off at Cafe Paris there in Reykjavik...cute waitresses.
And it's a good place to people watch.
Keep in mind that Iceland is very expensive. I ate at two different pizza places (both are good) and got a coke at each (I don't drink so I couldn't tell you the price of beer/cocktails). I paid about $20 at one and $25 at the other, and I believe that was before the 3% foreign exchange fee. The Hilton's nice...rate was 8900 ISK/night, which I think was equivalent at the time to around $140, but it's more of a business traveler's location. They do run a complimentary shuttle into town several times a day and there's a bus stop across the street.
PM me if you want more info...I'll be happy to look things up, where I went, what I paid (as long as I can pull my credit card statement up online), etc.