As has been said in other threads, bands like Green Day and Blink-182 aren't really "punk," they're "power pop." "Pop punk" is a misnomer, all they really pick up on is the high energy and simplicity. Green Day kinda poses as a punk band, or used to, but that isn't really who they are.
Some would say that punk died almost as soon as it was born, that it was all over by 1978 or so. It left a major legacy though, including the 80s hardcore bands and then all kinds of subgenres squabbling over who's more punk than who.
I would say go back to the first wave - Velvet Underground, Ramones, New York Dolls, Iggy Pop and the Stooges, Richard Hell and the Voidoids on the US side, and Sex Pistols, the Clash on the Brit side.