Help, I am studying abroad in Valladolid this fall. I arrive to Madrid at 1030pm and will be staying the night before I take a bus to Valladolid. What is a good/cheap hostal near the airport?

It's probably better to get a hostal downtown, since buses to Valladolid depart from Estacion Sur, which is just south of Atocha. That way you get to see a little bit of the city. It should be just be getting started by the time you arrive.

I´ve seen requests for info on accommodation near Madrid airport before, so I thought I´d note what I saw advertised in a regional paper this week.
There were 2 hostals advertised, both boasting climatización, baños and tv in their rooms (individual o doble) and are both located in Barajas.
Hostal Príncipe gives its tel num as 917477965 and claims to be located next to the airport.
Hostal Emilio has the number 913291752 and gives its address as c/canal de Suez 24, Barajas.
I suspect you will need to be able to speak Spanish in order to book a room, but at least you have an option if you need to stay the night in Barajas. Obviously, until a member of the board stays there and gives his/her opinion we won´t know how good these places are. No url was given in the anuncio, so I don´t know if they are listed on any website.