WELCOME TO THE BOARDS, sodapop!
When you are in Madrid, go to the Malasaña District (metro Tribunal).
It is just off a main street, Fuencarral, and close to Sol (maybe 15 minutes walking). On any given Fri or Saturday, you should see a bunch of people walking through the streets in that district, so just follow them. There are a couple of streets lined with bars of all kinds of music, mainly oldies rock, 70's, punk, and house/acid music.
There's one really packed bar, whose name escapes me right now, that has lot's of old posters of rocks earlier days. They played a lot of punk music. You'll know it when you walk into it.
So the Malasaña District your best bet for punk, that I can recall.
Now go, and sin no more......