The best of Madrid

Here is my list of the best of Madrid.  I have never been there, so I know some of my suggestions may be off.  So, I thought we could help each other make a best of Madrid list.  Please contribute if you know Madrid well, live there, or have spent a considerable amount of time traveling to Madrid. Thank you in advance.

-the best authentic/most unforgettable local travel experiences.
-non-typical, interesting/special experiences (full of original character), and unique only to the local area.
-memorable/dramatic scenery & landscape photography. Where do I find the best (viewpoints, city views, panoramas, skylines, sunsets, etc..)?
-the unique outdoors, hikes/hilltops/lookouts, and amazing views…
-lovely/charming streets,
-specialty/unique local cuisine, and gastronomy (under 15Eur/meal), the best freebies and/or anything else off-the beaten path.

Thanks again…(my list is located below)

MADRID

sights:
Placa Mayor, Espania, Sol, Oriente, Placa Ciebeles (Palacio de las Telecomunicaciones),
Retiro Park, Puerta de Alcala
Palacio Real, Catedral de la Almudena
Templo de Debod, Parque del Oeste (at sunset)
Plaza de la Paja
Atocha station (turtle waiting room)
Reina Sofia (free Saturday/Sunday after 2:30), just for Eu citizens or everyone?
Prado (between 6-8pm), same question regarding nationality?
Sundays -Rastro Flea Market, located in La Latina
View, 26th floor bar in Edificio de Espana building
Moorish quarter

exursions (inside):
Sierra de Guadarrama, Penalara peak
Aranjeuz,
Chinchon
Escorial/Valle de los Caidos, catch bus from Moncloa station in Madrid

excursions (outside):
Toledo, take bus from Madrid, (Mendez Alvaro) to foot of hill, walk up to Toledo, St. Martin’s bridge, Mezquita de Cristo de la Luz
Avila,
Segovia, c8 train, alcazar, asoguevo square, sunset at aquduct, sucking lamb, Cochinillo Asado

food:
El Cocido Madrile?o (the madrid soup)
bocadillo de calamares (where can I find a good quality calamari sandwhich)?
patatas bravas
Calle Arenal (comida para llevar), but what kind of takeout food is it?, Calle de Preciados (basement delis), sounds interesting but is it tasty?
Sopa de Ajo
Sepia con alioli
Boquerones en vinagre
huevos estrellados
torrijas
El Corte Ingles, chocholate covered figs