Now, as far as driving there and stopping on stores on the way, I'm pretty sure that's a big no.
You may also have a handgun securely encased or otherwise not accessible for immediate use anywhere in your car. It can be in plain view. It cannot be on your body, as far as I know. Securely encased includes snapped in a holster, so you could have it closed in a snapping holster riding in your side seat while you drive. A long gun does not have a requirement for being securely encased or otherwise not accessible for use.