Eight hour layover in Reykjavik

The National Museum of Iceland, near downtown Reykjavik, is very interesting. See http://www.thjodminjasafn.is/english/. Has a cafe if you want lunch.

Look at the Flybus schedule and see if you can take a nice leisurely dip in the Blue Lagoon - you should have plenty of time to do this, have a nice meal (since the Blue Lagoon is a tourist trap - albeit a wonderful one - you can eat and relax after your swim/dip) and get back to the airport well within 8 hours. http://www.re.is/DayTours/ Alternatively, you can stroll around in Reykjavik for a few hours - it shouldn't be too difficult to find somewhere to stow your luggage - just e-mail the tourist folks in Iceland to guide you. The Flybus is a very efficient way to get to/from airport via Blue Lagoon or City proper, and the bus is coordinated with each coming/outgoing flight. Just look at the schedule and see how much time you have for each option. I had a 3-4 day layover there and loved it!!! I came back a second time for a week a year later.

The Blue Lagoon is probably the best option to relax between flights. Reykjavik is relatively far from the International Airport in Keflavik (45 km). Net time which you would have for Reykjavik would be probably about 4 hours (immigration, transport there and back and you have to be at the airport 2 hours before your flight- maybe slightly less but not much) and that would be too short time to arrange and do the tour of Reykjavik. Reykjavik October weather probably won't cooperate, either. Also Blue Lagoon is much closer to the airport than Reykjavik.

Definitely recommend the Blue Lagoon above all else. You could spend hours and hours here and there is nothing else like it in the world. There is also a spa and a restaurant in addition to the pools and your admission will last all day. This would be my top choice, or if you would rather, bus into Reykjavik city and walk around the main streets, hit the Hallgrimskirjka (beautiful church) and have lunch and then head back to the airport.

As everyone else has said, the Blue Lagoon would probably be the closest & most relaxing choice.

The Lagoon is the easiest route. Reykjavik, while a nice town, is really just that: a nice town. The lure of Iceland is it's terrain and scenery and waterfalls and beaches and rocky coast and fjords and glaciers and geysers and thermal waters....the city is nice, it's fun, it's smart...but not spectacular. And, while the Blue Lagoon is a tourist trap I have never read anyone say it's not a great take. You'll walk through a lava field to get to it, see mountains in the distance and relax in warm, healing waters perhaps a sauna and steam, maybe a massage...what's not to like! And, you won't be stressing for time.
One thing, if you are travleing to Europe from the States, your flight may get in as early as 630am...the BL doesn't open until 10am....if that's the case and if you are traveling only with your carry-on you'll be out of the airport in 45 mins...(or less)...Reykjavik might be looking better and better! If so, write back and I;ll recommend a good breakfast place!

Thanks to everyone for the suggestions. I will be arriving at 6:45am on a Sunday and departing at 16:10 for Copenhagen. I've been to the Blue Lagoon website and although it sounds nice, it's not really my cup of tea. I'd like to see a little of the countryside and walk around a town to get a feel for things. I arrive pretty early and the days in October are shorter...I'll check with the tour company when I arrive to see if they think it's worth it. As always when I travel, I try to be flexible so I may just enjoy a nice swim in warm waters more than I thought I would.