I am flying from Memphis to Seville in March. I am scheduled to arrive at 8:05 am at Barajas in Madrid and to fly out to Seville at 5:50 pm. I will meet family members at Barajas airport, but they don't get in until 3 pm. So I would like to leave the airport and take the Express bus into Madrid, maybe spend a couple of hours in Reina Sofia. Is this practical? I speak fair Spanish, and assume my luggage will be checked thru to Seville, so I will just have a backpack with me.
Jordan,
You can certainly travel into the city & visit Reina Sofia for a few hours then grab lunch & head back to the airport.
The easiest way is to take the 'Cercanias' (commuter train) C-1 line from Terminal 4 (every 30 minutes), all the way to Atocha train station (travel time 25 minutes).
Once you reach the train station, you can walk to the museum which is not very far.
Hope this helps!
Edit: I forgot to post this link:http://www.aeropuertomadrid-barajas.com/transportation/madrid-airport-bytrain.htm