We have a flight from Pamplona to Madrid and will have about 6 hours to spend around the city before our connection to NYC on a Sunday in July.

Any ideas where we can store our luggage (one carry-on each) while we stroll around Madrid?

ttt

There are Left-luggage offices in T1, T2 and T4.

Price locker rental: all* or part of day, 2.85 € (big or small locker); two to fifteen days: large locker, 5 €; small locker 3.58 €. Warehouse after fifteen days: large locker 1.43 €; small locker, 0.72 €. Transfer to warehouse: 35.85 €. Special luggage, 3.57 €. Lost keys, 14.34 €.

There are lockers specifically designed to hold large objects such a bicycles, surfboards, etc.

Anything deposited at the left-luggage office has to go through x-ray control to check for dangerous elements or objects.

To use the left-luggage office:
- Ask for your own key at the desk. You have to identify yourself with your DNI (personal identification card) or passport
- Purchase a token from the vending machine (coins and notes accepted).
- Put your luggage through the security scanner.
- Open the locker turning the key in the indicated direction put your luggage inside and close the door.
- Enter the token in the slot and close with the key. Keep the key, it is proof of deposit.

* All or part of a day: period between deposit time and the following 24 hours.

Depending on which terminal your flight to NYC is departing from; you should leave a minimum of three hours to check back in once you've left the airport. You will have to go back through screening and collect your luggage. There's not much going on in Madrid on Sunday mornings, but you may be able to find someplace for breakfast, or just walk around until you have to head back to the airport.

Thank you, Robert2533.
Any idea how to find those services or what the term used, in Spanish, is so that I can be guided in that direction?

In Spanish, look for signs for the "consigna".