Madrid is certainly a fascinating sprawling metropolis, it’s very much worth exploring all the neighborhoods; each with something unique to offer. In order to get a good taste of the city, I would recommend visiting for a minimum of 4 or 5 days.
I would also recommend the following activity for a great day of sight seeing: start your moning with a big breakfast to help fuel a long walk, put on your sturdiest walking shoes and off you go...Hop on the metro and first stop “OPERA”, upon exiting, you’ll find yourself in Plaza Isabel II, very beautiful...
From the nearby Plaza de Oriente, you can already make out the stupendous Royal Palace...certainly worth a stop to snap a few photos between the well manicured flora of the gardens.
Skirting the palace you can also see the cathedral. Following Calle Mayor, you will end up in Parco Atenas: make sure to have a nice break near the kiosk...pleasant music, and palm trees; no better place to grab a coffee and feel swept away on a vacation far away from chaotic city life. The sun makes everything that much more spectacular!
After walking the Paseo de la Virgen del Puerto, and once you’ve reached the Principe Pio station, continue towards the Jardins de Sabatini (one of my favorite sights).
If after all that walking you find yourself starving, i suggest you head to Calle Carlos III and find: “Entrepanes – Café de Oriente”.
For an alternative, on Calle Arenal, there’s always “Jamones Ferpal”, very typical madrilena cuisine.
Finally, a few steps away, you’ll find Plaza del Sol...enjoy!