One of the best places to get a literal overview of Madrid if the roof terrace of the Círculo de Bellas Artes. It's especially wonderful if you go in the morning for breakfast when it's still cool and, if you brave the crowds, at sunset. It costs 3 euros to access the terrace and there are tables and lounge chairs as well as two bars serving breakfasts, lunches, drinks, and cocktails.
Personally, I don't enjoy the evenings when they try to make it something of a Euro-trash hang out but I will admit that the atmosphere is nice at night during weekdays and in August when there aren't many people. Just don't go on a Friday night ;). The rest of the time, it's spectacular. You can see literally everything in Madrid excepts the Royal Palace: Gran Via, Cibeles, Atocha, the Four Towers, the scenic church steeples of Huertas and the Barrio Salamanca, the Paseo de la Castellana, the Prado Museum...everything!
Anyways...if you're visiting Madrid for the first-time, this should definitely be on your list. It's a wonderful place that's popular among locals and not in a lot of the more traditional museum-and-monument guidebooks. I'd suggest heading there at 10am for breakfast. You won't regret it!
The gourmet experience is located on the top floor of the Corte Ingles department store on Gran Via. Enjoy spectacular views across central Madrid, whilst nibbling on a piece of manchego washed down with the standard small beer.
With the renovation of the Palacio de Cibeles and its re-purposing as an exhibition center and town hall, we can now not only enjoy the spectacular interiors, but also the viewpoint on the 8th floor which offers an entirely new vision of the Spanish capital. The views are panoramic, but the best part is the view of the Plaza de Cibeles with Gran Via and the Sevilla area in the background.
You can also see the other classic terraces in the area like the Círculo de Bellas Artes which is conveniently located in the same direction as the sunset.
To visit, you need to purchase a ticket ahead of time. The tickets cost 2 euros and they let people enter every half hour. If you want to see the sunset, it's best to check the schedule and get your tickets ahead of time.
If you're a photographer, remember that you can't use tripods on the terrace.
Following Bailén Street past the Royal Palace and Viaduct, you arrive at Las Vistillas Viewpoint, where you can contemplate the unbeatable views of the Almudena Cathedral, Casa de Campo, and, on clear days, the Sierra de Guadarrama mountains, which were the Christian-Moorish front during the Moorish Invasion. Las Vistillas was used as a look-out during those days to keep track of the advancing Moorish troops.