This isn't quite right.
Firstly, there are (at least - but this will suffice for general discussion) two systems, as noted: state and federal courts.
State courts are courts of general jurisdiction -- they can hear cases on state, federal and constitutional law. Federal courts have limited jurisdiction -- they need personal or subject-matter jurisdiction. For the purposes of this discussion, all we need to know is that Constitutional questions are within the jurisdiction of federal courts.
So, both state and federal courts can rule on the Constitutionality of state and/or federal laws. The question is the applicability of their authority.
State court decisions are only binding interpretations within the state - so, state courts are not the preferred venues for people to bring suit if they want to try to get a federal law interpreted as unconstitutional. Those cases almost always land in federal court (and when they don't start there, they are often removed there). [ADDENDUM: I should note that state supreme court decisions on Con/federal law questions are reviewable by the USSC].
So, point one, is that generally questions on the Constitutionality of a law begin in lower federal courts.
Point two, is that lower federal court opinions are appealable for two levels up -- the Circuit Courts and the US Supreme Court. So lower-court rulings are only final once they've either been affirmed by a superior court or the next level up has declined to review.
The other thing to note is that, except for the USSC, the rulings of the district (and the circuit) courts are only binding within their respective jurisdictions. So if you're talking about having a federal law declared unconstitutional, for it to be binding authority throughout the U.S., that decision needs to be affirmed by the USSC.
Clear as mud, no? =-)