We had two days to see everything we could in Iceland. We were exhausted from our flight, but were determined to resist taking a ‘short’ nap.
We made our way to the tourist bureau, where we got a 24 hour visitor’s pass, which got us free buses and admission to a lot of museums. In addition, we bought tickets for a 1 day guided tour the following day – "Golden Circle". The visitor’s pass got us a discount on the guided tour, so before we left the tourist bureau we’d already almost broken even on the pass!

Hallgrimskirkja, a cathedral at the top of a hill, towers over much of downtown Reykjavik. This was the only blue sky we saw while we were there.

What was ironic was that we saw this same scene being played out in Turkey later on in our trip, but not for show!
After a much-needed nap at the hotel, we headed to one of the public swimming pools: "Laugardalur" . This was no regular swimming pool. It was geothermally heated, like almost all of Iceland, and was more of a ‘spa experience’ than a pool. There was a few large hot tubs, a cooler swimming pool with lanes for swimmers, a huge bath-tub warm pool with a 6 story high waterslide emptying into it (with no adult supervision, and several "hot pots". The hot pots are like small circular hot tubs, with temperatures varying from 65 to 110F. All for $2 apiece – it was the only reasonably priced attraction in Reykjavik! We met lots of other tourists here, and it was a great way to wind down the day.
The following day, we took the Golden Circle Tour. We are usually averse to guided tours, but it was the best way to see a lot of the southwest of Iceland in a short amount of time (even our backpacker’s guide, Let’s Go, recommended the tour). The tour takes in the geologic and historic highlights of the area. We saw

Ahhh, much better. This is the Blue Lagoon, which is actually the runoff of a power plant. Not bad runoff!
Even on a rainy overcast day, this was a great thing to do, as it so warm. One last tip: even on a very short layover in Reykjavik (less then one day) it may be possible to visit the Blue Lagoon. It is located very close to the airport, and there are a few direct buses from the airport.