Hi---Just need a room for one night in order to be near the Madrid Barajas airport after a two-week stay in Salamanca at the end of September. Can anyone recommend a place that is simple and safe and inexpensive? Thanks so much!

never stay in places near Barajas, but hear good things about this hostal Cervantes
http://www.hostalcervantes.com/sp

HOpe it helps

Hostal Montecarlo 15 Gran Via is located next to a metro subway stop which you can take to the airport...it is good.

I stayed at the Hostal Cervantes about 5 years ago and it was fine . Clean for sure . They didn´t provide breakfast , but that´s no big deal as you´re only a 10 minute walk from the Puerta del Sol . The owner is a nice guy . I´m pretty sure it doesný have an elevator and it´s about 4 floors up . The street is small and you´re very near to El Prado etc.. . It´s basic , cheap .. I stayed there for 2 weeks .

then again if you can stay more central you wont have a problem getting to the airport with the metro.
http://www.infohostal.com/guia/madrid/madrid/alojamiento/8506/hostal-la-residencia-del-viso.html
the hostal La Residencia del Viso, near Nuevos Ministerios that is the metro that takes you to the airport. When I was looking for hostales folks told me this one was good.

another I have stay in previous years is the hostal La Plata, Gran Via 15 4B
http://www.hostal-laplata.com/laplataflash/home_textos.asp

you have zillions to choose from. Hope it helps