Calle de Santiago is from Calle Mayor /Plaza de San Miguel (it is in "Madrid de los Austrias").
I´d suggest you after the visit to the Palace return your hotel by :Plaza de España-Gran Via-Calle Preciados -Puerta del Sol-Plaza de Canalejas-Calle del Principe-Plaza de Santa Ana -Plaza del Angel (you can see handred of shops,bars,cafes,peoples ).
With this tour you will pass three different Madrid :Madrid de los Borbones(Prado area),Madrid de los Austria (Plaza Mayor,Santiago street) and
XIX century distric (Plaza de España, Gran Via,Sol)..
ABP