Madrid City Card?

Websites of museums and attractions participating in sightseeing-card schemes sometimes offer tickets not only at full price (and the common discounted prices for students, etc.) but also tickets for those with the sightseeing card. You may also sometimes find combination tickets that allow you to see two or more sights at a discounted price; I believe there's an art-museum pass in Madrid, for example. You'd have to check the individual attraction websites to be sure. If no luck there, you'll have to wait to buy tickets until you get to the city if you want to take advantage of the discounts. The Madrid City Card (MCC) website suggests that you will probably have to buy tickets to locally to qualify for the specified discounts (but that may be no great loss--see my comments below).

Most European sightseeing attractions are not so popular that tickets must be purchased in advance (yes, there are a lot of exceptions in Barcelona and some in other cities). I know some posters have recommended buying tickets to the Pardo and Royal Palace ahead of time, and they were busy enough in 2016 that I think you could run into something of a ticket line if you waited; however, they don't seem to have MCC discounts. I would certainly buy a ticket to the Monasterio de las Descalzas Reales ahead of time if you want to see it, because a tour is required, and the English-language tours have limited capacity.

Buying all one's sightseeing tickets before leaving home is not a risk-free practice. Your trip might get cancelled or delayed. Sightseeing tickets are rarely refundable.

As is fairly often the case with city cards, the MCC (https://citycard.esmadrid.com/en) doesn't seem all that exciting from the financial standpoint:

• Some of the listed attractions are free to all comers even without the card. That's apparently true of the city museums and the Temple of Debod, for example.
• The website implies the card gives you free access to the Prado late every day, but I believe that is true even without the card. That sort of thing really turns me off and makes me very disinclined to even consider buying the card.
  
• The website says the card will "soon" allow you to skip the line at the Royal Palace. (Note that it doesn't say you save money on the ticket.) When is "soon"? Will this benefit be in place by the time you travel? Who knows?
• Some of the discounts are quite small (10% or 20% is really nothing) or are for places I suspect would be way down the list of priorities for most tourists.

This card seems to be mostly a transportation pass with very marginal additional benefits a traveler would actually use. There's nothing wrong with a transportation pass if you need to use the buses or the subway system a good bit, but usage of local transit may depend to a considerable degree on how much you enjoy walking. I think it's only in Berlin (a sprawling city with really scattered sights) that I've gotten my money's worth from a transportation pass--but then I always prefer to walk if possible, so I can enjoy the city I'm in. Those with mobility challenges and those on very short visits may get a lot of value from a transportation pass. However, for Madrid it's especially worth noting that the Prado, Reina Sofia and Thyssen art museums are fairly close together; a walk encompassing all of them is just under 1 mile. A visitor could spend 1-1/2 days or so on intense visits to those museums and only use transit twice per day (or not at all if he/she happened to be staying down in that area).

My recommendation is to consider this a transportation pass. I looked online but couldn't immediately find the current fares for Madrid transit. Perhaps one of our posters knows the current cost(s) per ride. You really need that information to evaluate whether there's a financial advantage to the MCC.