You better come flying to Madrid. Train is very expensive and you'll probably find offers in flights (I recommend you www.terminala.com , and the company Air Europa, most Spanair flights are delayed and Iberia arrives at T4 in Barajas and a taxi costs between 10 and 15 euros more than coming from T2). And the flight is faster than the train.

I know Hostal Tokio, near Gran Via. It's cheap, clean, and comfortable.