I'm not sure what the penalty is for CCW in a place you shouldn't---any ideas.
Yeah. Find out. Some states it's a felony, meaning big time penalties and loss of gun rights for life. Go to packing.org and you should be able to find out.
Regarding leaving your gun in a car, I agree, that is to be avoided whenever possible. Get one of those small handgun safes and bolt it to the floor of your car. You can almost certainly find one that'll fit under a seat. Sure, it could still be stolen, but it'll be much less likely. But if it does get stolen, you'll be able to tell the cops the extreme measures you went to. They'll find that refreshing, and you'll feel like such a damn fine citizen you won't be able to stand it.