The airport is linked to the city via subway lines and its not too complicated of a system.  I don’t remember exactly, but it maybe takes 20 mins to the city.  Lock your luggage and go exploring. 

Being that Madrid wasnt in my plan to see. What is there to see or do in the city???

For something a little different – Go to the arabic baths – great way to get ready to sit on a plane again. You need a reservation but you can do that online. http://www.medinamay….

C

 
Central Madrid is really easy to get to from the Airport via metro, it won’t take more than an hour getting there. 
 
In 20 hours you could see a bullfight, take a salsa lesson & visit a brothel and still have a few hours to get back to the airport on time.

Please do not spend 21 hours in an airport. The subway is very nice and you can get prety much anywhere in less than 45 minutes. There are some museums, and nice parks, you could check out the palace, or just wonder around and see some plazas and eat tappas. It will not be hard to have a good day and still catch your plane out. 

NJLANDROVER writes:

There’s time to explore, if you have a plan.  It might be helpful if you tell us when this layover will occur: i.e., Month, Day, and time of day of your arrival and departure.  

There are ‘daytime’ things (tours, etc.) and ‘nighttime’ things (Tablaos de Flamenco for example).  Late Sunday afternoon or any day during Madrid’s San Isidro festivities in May you might see a Corrida de Toros.

If Madrid is your Airport of Entry to the EU, you’ll have to Clear Customs and Immigration there; and just make sure to leave yourself enough time to get back to Aeropuerto de Barajas and thru Security before your flight departs    

I will be landing October 2nd around 9:00 am.

I would just go to the city center and start walking (might want get a map though).  Have lunch, take a few pictures, enjoy the day. 

 
The best advice.
 
And it’s a very walkable city.  What time of the day will you be arriving at Madrid Barajas Int’l, and what time will you be leaving?  As IrishNed mentions, remember to take into consideration customs and passport control (which may or may not be swift), and then on your way out, checking in again (if you neeed to; do you?), and going through security again. 
 
I would say to take the metro to city center (maybe any of these stops: Plaza de España, Banco de España, Sol, Ópera), and just explore the city center…my absolute favorite is to explore old Madrid, the area around Palacio Real, Amudena Cathedral, and beautiful&nbsplaza Mayor, east towards Puerta del Sol (encompassing sections of the charming Latina and Los Asturias districts).  With a map in hand, and some reading, you can find out a lot about Madrid’s very varied city center, and explore it by foot.  If this is summer time, after lunch, spend a few hours in the Prado Museum during siesta time, or in the Centro de Arte Reina Sofia (of course, check for opening hours, because Prado closes early on Sundays I think). 
 

I will be there from 9am (if i land on time) till 6am the following day. I have to check back in they recommended approx. 2 hours prior (so 4am) and go through security.