From the airport
Train: C1 to Chamartin then C3 to Puerta del Sol. It's a 35 minutes trip. If you are in the city for a few days buy a T-10, Multi-person card for 10 journeys, (€12,20). It works on the bus too.
Taxi: It's a 20-30 minutes trip and is around €30.
Aerobus shuttle: Drops off at Atocha, Cibeles (night) and O'Donell-Doctor Esquerdo to Airport T1,T2 and T4 and costs 5€.
From all terminals of the airport (T1, T2, T3, T4), take metro line 8 to Nuevos Ministerios, the last stop. There, change to metro line 10 in direction Puerta del Sur. Get off at Tribunal, and change to metro line 1 in direction Valdecarros. Get off at Antón Martín and walk to the hotel (270 m).