Here are a few options that we hope fall within your budget and may be of use to you.

The Tres Cantos area, although on the outskirts of Madrid, is pleasant and quiet, and has direct access to the university via the C4 Cercanías line (a 7-minute journey) and to the city centre of Madrid (half an hour from Sol station on the same Cercanías line). We have found four options near Tres Cantos station:

VP Jardín de Tres Cantos 

Exe Tres Cantos 

Ramada by Wyndham Madrid Tres Cantos  

Eurostars Madrid Foro

Close to the airport, you will find the Hotel Don Luis. To reach the university, you would need to take the Metro line 8 to Nuevos Ministerios and then the C4 Cercanías line, or alternatively take the 827 bus directly to the university (approximately 40 minutes; by taxi it would be around 15 minutes depending on traffic).

Further options, should you be able to travel by taxi, are the Exe Convention Plaza Madrid, in Las Tablas, and the Hotel Golden, in San Sebastián de los Reyes. This last-mentioned town may also be a good accommodation option in its own right if you find something near the station, as it is only 7 minutes from the university by Cercanías.

Finally, at a somewhat higher price point, there is the Hotel Madrid Río, very close to Legazpi underground station and the city centre. From there you can travel to Sol (7 minutes) and at Sol take the C4 Cercanías line to the university (20 minutes).