El Tigre!!! Great drinks and even better and bigger tapas.

That is a big question, because I think of Madrid as much more than Tapas. Some of my favorites are

Taberna Tempranillo

Taberna Txacolí

Mercado de San Miguel (there are a number of other markets in town that are also fantastic.

StreetXO - Not tapas but a must in my opinion

If you just walk down Calle Cava Baja it is lined with tapas places everywhere, you should be able to find anything you like there. 

There are a few other posts on here that cover similar topics to what you are asking, check them out and you will have plenty of good recs. Here is a good one.

The best that you can do is visit, multiple bars. 

In spanish say "vamos de tapas" and you with your friends visit one bar if don like go for another one, taste the tapas and go to another one...... thats really cool.

Ciudad Condal

Also known as Ciudad Comtal. Literally best tapas place I've been to ever and it's honestly very affordable!

First, head to La Casa del Abuelo for their famous garlic shrimp, then head to Casa Labra for fried cod and fried cod croquetas. Then, head to Las Bravas for some patatas bravas. Finally, try the meatballs El Madroño and they'll give you a free shot of liquor made from Madrid's emblematic official tree. All are within walking distance. A little farther away, try the salmorejo at Bodega La Ardosa in Malasana.

Hi juan,

There are many fancy tapas restaurants around La Latina. I specially like Juana la Loca Pintxos-Bar and a few ones in Calle Cava Baja street such as La Chata, a very tipical Madrid tapas bar still run by a very short woman.

Prices are not as cheap as they used to be but is still worthy.

Careful with pickpockets specially in the metro!

Enjoy!

You should try Casa Julio croquetas.

Lateral in C. Velazquez. A must.

Our favorite one is El Tigre. Delicious tapas and huge glass of beer or sangria, back in May we paid Euro 5 for 1 liter!
We also liked  Museo del Jamon,  great deals for beers and good "montaditos" and a lot of jamon !!!

Sidrería El Tigre