I'm looking for punk bands that utilize a lot of bluesy riffs/leads, as well as Chuck Berry-ish stuff. Stuff like Gang Green, early Suicidal Tendencies, and the Dicks. I'd like the bands to lean more towards Hardcore, but anything goes.

Badr Vogu is an awewsome crust/doom/blues hybrid. Should be just what you're looking for. They just put out a new album this month which will probably be up there at some point too

Sure this is an obvious choice but Minutemen might be up your alley. Immortal Lee County Killers are also a good band to check out.

My friends band Flip Shit might be what you want as well. Rock and roll meets early 80's hardcore punk. Here ya go.