Personally I HATE EasyEverything. It is crowded, the flatscreen monitors are about six inches from your face and give me a headache. Thieves LOVE the place because there are so many people occupied with their stuff ready to grab. It is a commercial type of place. There are many smaller, more secure and much better internet cafes in Madrid. By patronizing them you support locals, not some huge corporate EasyEverywhere. If you want to shout "I AM AN AMERICAN TOURIST!" then EasyEverything is for YOU! If you want to meet locals, then go somewhere else.
There is a small Internet Cafe in the building caddy-corner from Plaza España(on the northeast side -- the metro entrance is just in front of their entrance), on the fifth or sixth floor, in the very back (take a right as you get off the elevator or from the stairs) run by a man from Ecuador named Diego. There you will be safe, can relax, they have softdrinks, water, discs, FAX, etc. Personally I love the place because, before they moved to this location they were just off Puerta del Sol, across from MacDonalds, and I met my (future) wife there! How's THAT for a recommendation!
I know it is easy to go to the tourist joints, but why? This is why MadridMan's website is here, to clue you into the real deal.
Take a chance and do as the locals do, go where they go, eat what they eat, etc. I remember a woman I met once from L.A. who was upset because Madrid wasn't like L.A., and they didn't speak English! So stay in L.A.! I made my excuses and split. If you get away from the tourist traps you will have the time of your life, guaranteed, and probably make some incredible friends for life. Who knows, maybe, like me, you will realize that you cannot any longer live anywhere else and move here permanently. Just a little warning
. I apologize for the lecture, but that is how I see it.