You should take metro form Barajas airport to Nuevos Ministerios stop (Line 8, pink, travel will take 15 minutes). This metro station is in the middle of Paseo de la Castellana, the main street of the city, you can take bus 27 to Cibeles circus (it will take another 15 minutes), where you can see Banco de España, Puerta de Alcalá, Correos headquarters, Prado Museum and walk to Sol too. Ejoy it