In addition to the Royal Tapestry Factory and the Royal Palace (their Armory is interesting) you might do the hop-on-hop-off bus early in the visit. This will give you an overview. I have not taken this bus, and have heard that some people don't like it, but it will get you around to various places.
If you have not planned to go to Toledo (photo 2), you should take one day to go there. And there are day trips to places like El Escorial and Segovia which are also possible, but if you were going to do one day trip, I'd recommend Toledo.
There are the Teleferico cable cars or you could take a guided tour of the Real Madrid stadium
You might plan to have lunch at the Parque del Retiro (photo 4) which has a boating lake and fountains. On Sunday’s you’ll also see Punch and Judy shows, tarot card readers and stalls selling candy floss.
If you are there on Sunday you must also go to El Rastro, the outdoor market (photo 5)
Fondest memory: Even if you don't care for art museums, you really have to look at the Prado. I particularly like looking at the Spanish artists, or the ones that painted in Spain (like El Greco). Goya has some very Goth stuff there. I also like looking at the Bruegel's even though he's not Spanish in the least. I think if you limit your time there and pick one area to go look at, a museum visit won't be too bad
I've always been sorry that I did not get to the Reina Sofia Museum where Picasso's Guernica is exhibited.
Former capital of Spain, Toledo is certainly one of Madrid's better daytrips. The city historic center, with its remarkable medieval flavor, was designated by Unesco as a world heritage place, and thus ensuring an endless succession of tourist shops, tourist restaurants and a healthy dose of traffic jams due to the presence of tour buses in the area. However, not being an "off the beaten path" location doesn't conceal Toledo any of its multiple attractions: The gothic cathedral, the imposing Alcazar, countless museums... this is a location that deserves a whole VT page (working on it ;-) )
Fondest memory: http://www.virtualtourist.com/m/3c2c4/3db3e/
Favorite thing: Two mayors highlights came to my mind when recalling Segovia: The harmonic way in which the 2000 year old Roman aqueducts fits into Segovia’s city center, and the exceptional meals that the local gastronomy offers (do not miss the sucking pigs there). I guess the first highlight if the one that attract foreigners to that beautiful Castilian city, while the second one is the reason for many inhabitants of Madrid to take the 100 km. Road to Segovia every Sunday (local argot often refers to that people as "Domingueros") ;-)
To get a quick and comprehensive image of Madrid there are tourist seight-seeing buses.
You can choose between three diferent routes:
Ruta 1: Madrid historical
Ruta 2: Madrid modern
Ruta 3: Madrid monumental
Each bus will pass 15-20 different spots and you will be given information in English about them.
You can combine 2 or 3 routs and pay less if you make them the same day.
My tip is to make 1 or 2 of the routes in the evening and you will see the buildings enlighted which is very beautiful.
There are some stops when the bus take up and leave passengers and you can leave the bus whenever you like.
Of course those tours are not in any case detailed, but you will get familiar with some of the orientation points in Madrid.
Placed in the northern mountains of Madrid province, San Lorenzo del Escorial it's a highly recommendable day visit if you want to escape for a while from Madrid intense activity (not to mention the traffic). There you could enjoy a visit to the famous Monastery, as well as wonderful natural views of the beautiful valley in which the town of San Lorenzo is placed. By the way, it's full of tourist during the weekends, so that's probably the days in which you wouldn't want to visit the place. ;-)
Fondest memory: Please, visit my Escorial VT page for more info.
If you have enough time, keep a whole day to visit Toledo. This old town, 1 hour away from Madrid is exceptionally well conserved. Walking by its streets takes you to the XVIth century. You can wander the same charming cobbled streets and visit the ancient shrines that once hosted leading scientists, philosophers, poets, and artists. Sadly, many were Jews who were forced into exile in the late 1400s. But it was Toledo's atmosphere of antiquity and mystery that attracted the painter El Greco, who made his name here -- along with some of the nation's finest metal workers, who still produce world-famous swords.
The city fell to the Romans about 193 BC and was named Toletum. From about AD 534 to 712, Toledo was the capital of the Visigothic kingdom in Spain and because a great ecclesiastical center. After its conquest (712) by the Moors, the city became an important Moorish center and in the 11th century the capital of a short-lived Moorish kingdom (1035-85). In 1085, after a memorable siege, the city was captured by the forces of Castile and annexed to the Castilian realms, of which it was made the capital (1087-1560). From July to September 1936, during the Spanish Civil War, rebel forces in the Alcazar were besieged for 70 days by Loyalist, or Republican, forces.
Fondest memory: See transports to Toledo at my "Transportation" section.