Another store (generally located near Hot Topic in malls) is Spencers. Also good for accesories and t-shirts, as well as posters and hats. Just try to stay away from the back of the store if you're not really into the whole sex-related humor thing. Or sex.
Online, try zumiez.com (good for everything really, though the girl section is pretty girly, just as hottopic.com).
Also try akumunk.com (good for everything as well with cheap shipping, and pretty cool t-shirt designs).
Lip-service.com. Big one. Hot Topic actually gets a lot of their stuff from here, but UNLESS YOU ARE A VERY FASHIONABLE PERSON, DO NOT SHOP HERE. It's cyber-goth, cyber-punk, etc, filled with leather and other such dark fashionable clothes. Unless you're really going for an insanely dark look, do NOT go there.
infectiousthreads.com is awesome as well, with pretty cool plaid pants and kilts for guys. HOWEVER, some of the tops are a bit hooker-y, so don't wear if you don't want to be called as such, or worse.
For accesories, try Claire's. Awesome stuff, but not just a punky store. And sometimes they have awesome sales like getting 10 pieces of jewelry that were already marked $10 or under for $10 altogether.
And if you really don't want to spend too much money, check thrift stores (Salvation Army generally has some cool stuff, same with army thrift stores), as well as Wal-Mart and Target.
Try combinations of above stores, or just go to any regular clothing store and punk it up a bit by ripping shirts and adding some homemade accesories (try hemp jewelry) or stuff from Claire's, Hot Topic, etc. Try to get your own style: that's what punk's about, nowadays.