The Prado; essential art viewing.
And there’s a cablecar from near the centre out over a large park, which was well worth visiting when I was there (a while ago, now). Also a great museum of armour fairly near where it sets off from.
skip the prado (if you need to choose) and go to the Reina Sofia, just like how 'd’orsay is better than the louvre. Also, spend some time at the big park behind the Prado (Recreativo?)
Also take some time to visit Retiro Park which is quite lovely.
The Bernabeu Soccer Stadium is one of the most impressive in all the world, so go and take a tour and snap some pictures.
The “old” part of town, Puerta Del Sol is a nice lively place to see all different types of Street Performers and cool shops. However be very careful with your wallet in this area as pickpocketing is common.
Near Sol, a tour of the Royal Palace is also a must, quite impressive.
I like the Thyssen museum more than Prado, but that’s more a personal choice.
If you are going to be in Madrid for 4 days, take an Afternoon and visit the near by town of Toledo, for which there are plenty of different tours to choose from and is worth the time.
Madrid has 3 different tour buses to choose from, all which take you to different places in the city.
Unfortunately the bus tours, in my opinion, are not comprehensive enough, but if your only going to be there for 4 days, then it’s a quick way to watch important parts of the city.
There’s many bars and restaurants which offer Menú del Día (daily menu) which can go from 6€ to over 20€; it’s more limited than eating a la carta (off the full menu) but generally quite good. The cheapest places may offer something like
1st dish: your choice of
green beans with potatoes
spaghetti bolognese
white rice with tomato sauce
lettuce salad
2nd dish: your choice of
steak
chicken
cod
plus water, bread and dessert.
The more expensive places offer fancier fare.
El Prado has already been mentioned: it’s on el Retiro, so you can kill two birds with one stone.
Are those 4 full days, or is it “arrive on the 1st, leave on the 4th”? If it’s 4 full days, you may want to take a day trip to Toledo or Cuenca (Toledo is more common), both can be done with the train from Atocha station. There’s guided bus trips to Toledo, you should be able to book one through your hotel.
Years ago, I offered a trade to an American friend who was working in Madrid at the time: I’d pick two museums, one “for me” and one “for him.” The one for me was El Prado (by the way, it has three doors and on Saturday it’s free, if you see a long line at a door just go to a different one); the one for him was the Military History Museum, which sadly isn’t very prepared for tourists (ie, you’ll enjoy it a lot more if one of you can read Spanish) but still has a lot of interesting stuff.
If you can get a “Madrid de los Austrias” tour, do. Madrid was an ass-of-the-world village until Felipe II decided to move the capital there from Toledo, the parts shown by those guided tours are the historic centre. The cathedral just got finished, as Spanish cities go our capital is a Jane-come-lately
There’s the usual museums, theme parks, etc. but with four days I think you can do much better by walking around Puerta del Sol (nice shopping) and el Retiro.