Both are okay, but I would want to say: "Never take anything from someone you don't know." That way you're not using "any" twice in the same sentence. To me it sounds better :)

I would be tempted to say: Never take anything from anyone *that* you don't know. Never take something from someone *that* you don't know. Both sentences are ok however. In particular, the first sentence has more emphasis: "Never take //anything// from //anyone// that you don't know."