Barrio Salamanca is a relatively modern neighbourhood, built between 1860 and 1927, so there is very little here that is truly old. Some of these places are on my Google map here.
Another famous neo-Mudejar building is Casa Árabe www.casaarabe.es at 62 Calle de Alcalá.
A more colourful example of this architectural style is on the corner of Calle Goya where it meets Calle Alcala.
On the north side of the El Retiro park at 83 Calle de Alcalá, is the Neo-byzantine Church of San Manuel y San Benito which contains some famous tombs. The church could easily be mistaken for a mosque.
Back in Guindalera, Calle de Castelar has some unusual little villas known as ‘hotelitos’. Nearby Calle Roma and Calle Belluga have some bits of neo-Mudéjar architecture.
South from here, at 47 Calle del Dr. Esquerdo, is La Casa de Abejas, with a swarm of bees on its facade. I’d be intrigued to know how much business this ‘apicultura’ (beekeeping) shop does in such urban surroundings.
At 26 Calle de Goya is the brilliant white Basilica de la Concepción de Nuestra Señora concepciongoya.archimadrid.es/ (opposite the Hotel Catalonia Goya).
Lots of other nice buildings dot the neighbourhood.