Whirlwind 1/2 day visit to Madrid- please tweak if needed!

I took the bus from the airport to Atocha, but the train might be faster. It probably depends on your timing. I'd research both options and look at my watch as I headed out of the airport.

Where would you pick up your walking tour? I'm guessing it might be somewhere like Plaza Mayor, which is quite a walk from Atocha. Also, I found it a bit challenging to get myself oriented as I walked out of Atocha Station. A map on your smartphone may speed you on your way.

I believe you'll be tight on time for the 11 AM tour, so be sure you know precisely where you are to meet the guide and how to identify him/her.

I think the walking tour is a great idea, but if for some reason it doesn't work out, Rick has a good self-guided walking tour in his "Spain" guidebook.

Just about any walking tour will take you near if not actually to the San Miguel Market, which is very near Plaza Mayor. It's a great spot for upscale tapas, though you can also pick up a cup of cut-up fruit, and I think there must be pastries, too. So you could grab a quick breakfast there before your tour if you have time, then tapas after the tour. On some days and at some times the market can be quite crowded. I assume it's a place you need to be wary of pickpockets, so guard your wallet/purse/daypack.

If you have extra time, I enjoyed the botanical garden that's not very far from Atocha. The entry fee is fairly modest--maybe 6 euros.

Well, as it is what it is... there's not much more you can add or do in that timeframe. If anything, take into account rush hour in the morning (meaning the metro can be packed). Yet, certainly, it'll be faster than a taxi -at that hour.

As for lunch, have a look at some options here: http://www.timeout.com/madrid/restaurants

Yet being in Madrid you might want to try one of their most famous restaurants: Casa Lucio which isn't cheap but it's worthwhile. A regular hub for celebrities both local and foreign, you can try many delicious Castillian specialities there. Their signature dish, believe or not, is "huevos estrellados", a humble sunny side up eggs, scrambled over French fries. Peppers, sobrassada or jamon can also be added to this dish to make it more delicious. A substantial equally luxurious rival is Casa Botín, the oldest restaurant in Spain, established in 1725.

There are obviously many other options, but considering you're not in Madrid every day, one might consider splurging in one of these two pinnacles of the city.

Thank you for you for the advice! Do you anticipate there being rush hour traffic on a Saturday morning?

Not... in principle. I lived for a while in Madrid many years ago but I can't ensure traffic patterns continue to be the same :)

Any tour (free or not) that offers to show you historical events such as Alfonso XIII’s anarchist attack, the Spanish Empire, the Spanish Inquisition, or the Spanish Civil War, needs reconsidering.

I would do a walk on my own (with internet notes)...
Real Basílica de San Francisco el Grande >> Royal Palace (outside) & Sabatini Gardens >> Plaza Oriente >> Plaza Mayor >> Puerta del Sol >> Gran Via (Metropolis) >> Plaza Cibeles >> Puerta de Alcala >> El Retiro Park >> Atocha