If you're looking to get into the city center by public transport, it'll take about an hour to 90 minutes.
This is a good option for those who are in town for a visit, but are fed up with the noise in the city center (no matter where you stay).
Hotel Barajas Plaza is located just off of Plaza de las Hnos. Falco y Alvarez de Toledo (a picturesque square in the middle of the old quarter, with a nice fountain and a nest of storks), which is ringed with several options for eating, drinking, purchasing snacks, etc. Wi-Fi is available at many of these places, as well as English menus.
Another benefit about the location of the hotel is its proximity to the bus stop - from here, catch the 101 bus to the airport, and you're at T1 in 15 minutes; catch the 115, and you can make the Linea 5 connection at Canillejas.
Also, arriving here from the airport is a breeze; catch the 101 from T1 or T2 and get off at the last stop (be sure to wave the driver down, or else he may not stop!)
The Barajas metro stop on Linea 8 is about 800 meters away, but it's a pleasant walk.
As for the room, the facilities were nice: comfortable bed, roomy bathroom (with bidet and bathtub), plenty of closet space, and it was so quiet.
Noise is a main complaint for visitors staying in Madrid. Here, this is not the case. Even with the proximity to the airport, the sound of arrivals and departures was surprisingly barely noticeable.
It's the best sleep I've gotten during a stay in Madrid. At 40 euros for a quiet room with en suite facilities, you can't go wrong.