Visiting sights in Madrid after tour

• Palacio Real (Royal Palace) is an enormous palace, one of the biggest in Europe, with scorching plains of concrete around it. Though it is the official residence of the King of Spain, the royal family does not actually reside here and it is generally used only for state ceremonies. The Royal Palace is considered to be one of the most emblematic and beautiful buildings in Madrid, not only for its location on a bluff overlooking the river valley but also for its architecture and the artistic treasures to be found in its rooms. A simple one-way tour of the palace (both self-guided and guided are available) takes you up the grand stairway and through the lavishly decorated state rooms with their elegant tapestries, frescoes, porcelain, carvings and added decor like china, silverware, medals, etc. From the courtyard you can access the Farmacia (Pharmacy), which contains hundreds of bottles of early medicines and a reconstructed laboratory, and the Real Armorial (Royal Armory), a two-story collection of medieval weapons and armor. Explanations in the armory are in Spanish only, so do not expect to understand much unless your know the Spanish names for all that medieval weaponry. The lines to get in are very long, especially on Wednesday when the place is free - try to go early. Photography inside the palace is not allowed. 

• Catedral de la Almudena, This massive cathedral faces the Palacio Real. Finished near the end of 20th century, it is where the Princes of Asturias Felipe and Letizia were married in 2004.  
• Reina Sofía National Museum and Art Center, Houses Madrid's best collection of modern art. It includes many of Pablo Picasso's most revered works including the renowned Guernica. The Reina Sofía also houses masterpieces by Miró, Kandinsky, Dalí, Bacon, and more. I entered 7 pm for free, but only appreciate the work of Picasso's. the rest was too morden for me.
• Museo del Prado, One of the finest art collections in the world and the best collection of classical art in Madrid. It includes many different collections: the Spanish (El Greco, Velázquez, and Goya), the Flemish and Dutch (Rubens, van Dyck, and Brueghel), Italian (Botticelli, Tintoretto, Titian, Caravaggio, and Veronese) and German (Albrecht Dürer, Lucas Cranach, and Baldung Grien). Some highlights not to miss at the Prado: The Bosch masterpiece The Garden of Earthly Delights, The famous Velázquez piece Las Meninas, The Black Paintings and The Third of May 1808 by Goya, Adoration of the Shepards by El Greco, and David with the Head of Goliath by Caravaggio. I got in free after 6 pm twice to see each paintings and the descriptions. No photo was allowed.
• Thyssen-Bornemisza Museum of Art Contains a large art collection including masterpieces by Monet, Goya, Degas, Renoir, Van Gogh, Picasso, Mondrian, Bacon and Lichtenstein. I run via the collection in half an hour for free due to my time constraint.
• Caixa Forum, A private museum of contemporary art and culture that is particularly well-known for the "vertical garden" by Patrick Blanc installed on a wall in front of the museum, as well as the quite special architecture of the building itself. 
• Museo de América, An excellent museum houses thousands of artifacts that were taken from the Americas. The exhibit displays objects from many native cultures from before European conquest to colonial times and beyond. The quality and quantity of the collection are way beyond those mesuems i visited in south and central Anerica. The Tesoro (Treasure) de los Químbayas, a collection of gold objects was given as a gift by the Colombian government. Also of interest is the Tudela Codex, an Aztec law book from the 1500's. The mammy display was so spooky that i was almost checkened out without photoing. ( I am a mammy fan but was never left alone with mammy in a huge room without other people.) However, most explanations to the objects on display are in Spanish only.