Madrid layover

You could take the airport express bus to Cibeles (5 euros - about 20 min), then catch a hop on hop off bus tour there to get an overview of the city (I think it was 20 euros when I took it). The route is about 90 minutes and will show you both old and new parts of the city. You can get off anywhere that looks interesting, then catch the next one that comes along. A tour at the Royal Palace will take about an hour (don't miss the armory), walking through the Plaza Mayor can take as long as you like, the same for Retiro Park. Just make sure that you allow travel time back as well as plenty of time to get through security back at the airport (in May it took me about two hours - I allowed three).

You'll have to clear customs, so allow time. Use a taxi for efficiency. Decide what you want to do. If it's see great art make a bee line for the Prado. If it's eat and stroll the Mercado San Miguel and the Plaza Major, which are next to each other. Just fresh air and nature, Retiro Park. But, whatever you do, leave enough time to get back as rush hour traffic can be abysmal.

A taxi from the airport is 30 euros (set price). You go through immigration upon landing, which is relatively quick. Customs is a walk through the "nothing to declare" door - no time at all.

And consider the RS Snapshot Madrid book. It's about $12 on this site. Lots of good tips. I don't know about luggage storage, maybe others do.

The internet tells met that there is luggage storage ("Consigna") at the Atocha station in Madrid.

You don't say whether you have the layover on entering Europe or leaving it, but either way, you will clear passport control (immigration), not customs, which is basically just a matter of walking through the "nothing to declare" door, anyway. I have never looked for a "left luggage" office at the airport, but if there is one at Atocha, you could take the Airport Express bus there, check your bags, then take a taxi to the city center (or walk it). From there you could catch a HOHO bus, see the Royal Palace, or whatever.

Gary,
You don't mention if you're connecting to a domestic flight (within Europe) or an International flight, but in either case,
you need to be sure to give yourself enough time to get back to the airport so you don't miss your flight.

You should be back at the airport 2 hours before a domestic flight & 3 hours before an International flight.

• According to the this website about Madrid-Barajas Airport, there is
  left luggage at the airport, located in Terminals 1 & 4. Scroll
  almost all the way down to see this information. You can click on the
  tear shaped icon (to the left of the terminal #) to see its location
  on a diagram.

• Here is more information:
  http://www.aeropuertomadrid-barajas.com/eng/left-luggage-office.htm

I have not left my luggage at the airport, but have left some luggage at the Atocha train station.

You can get to Madrid via taxi, bus (Airport Express) or Cercanias train: http://www.aeropuertomadrid-barajas.com/transportation/madrid-airport-bytrain.htm