Layover in Madrid

I don't know about luggage storage at the airport, but that service is available at the Atocha Railway Station. There's both bus and train service from the airport to Atocha. The Big 3 art museums are near Atocha, but since this is apparently your arrival point after an overnight flight, I would not want to tackle a museum. Retiro Park (free) is near Atocha, as is the Botanical Garden (entry fee). You could also head to the area around Plaza Mayor and enjoy tapas at San Miguel Market. Rick has a Madrid walk covering that area in his book.

Me, I'm a zombie after a transatlantic flight, and I'd be sorely tempted to get a day room at a hotel and sleep for several hours.

Christine,

There are two left luggage facilities at the Madrid Barajas Airport, but I don't have any personal experience with such since I've only left my luggage at the Atocha train station.

If you decide to venture out to the city (upon arrival) make sure you give yourselves plenty of time to return to the airport, pick up your luggage, and go through security again.

Your "8 hour layover", may not quite be this long.... You need to figure that it will take some time to get off the plane, to retrieve your luggage, to go through passport control, etc, etc...

Having said all this, I really don't know how much time you'll have, before having to return back to the airport...

I think you can do it if your flight is on time and you aren't delayed in going through immigration. Lets say getting off the plane, getting through immigration and getting to transit takes an hour (total guess, I've usually done it in less). Go to the express bus to Atocha station, drop your luggage there (another hour including finding the luggage storage). From there you can do something. You are close to some of the museums but since you go to Madrid later, I'd save those for more time/less jet lag. Perhaps go to Retiro Park to get some sunshine, walk around, find a square and get coffee.

You need to get back to the airport 2 hours ahead. This means getting luggage and leaving Atocha 3 hours ahead. Given that I just estimated that it takes 2 hours to get through the airport and to the station...you have 3 hours to play with. Seeing a couple things in Madrid can be done in 3 hours. And I am very conservative on timing - you will likely have more, barring long lines at immigration.

Of course you will be tired and might prefer buying a lounge pass and hanging out at the airport!

Thanks for the feedback everyone! After talking about it further, I think we may just play it safe and buy a pass to one of the airport lounges and try and get a quick nap rather than pushing ourselves. We are on a 14 day trip, so no point getting exhausted the first day.