What is this nonsense about locking up the ammo separate from the firearm? There is no such provision in FOPA. What is required is that the firearm be kept in a locked container. You may lock up your ammo, but there is no provision that it be kept in a separate container.
Second, we have to distinguish between carry and possess. In almost all states, you may possess a weapon (not otherwise banned by state law) on private property and in a locked container in your vehicle while traveling, but may not carry that weapon loaded or on your person in public. New York is a special circumstance. NYC and NJ police in particular refuse to acknowledge legal carry under FOPA, so unless passing through, don't take a gun there because in any event you will not legally be able to take it out of its locked container. With Illinois' FOID law, the rule may be essentially the same.
California and Massachusetts have restrictions on mag capacities such that you may be able bring the gun, but no mag greater than 10 rounds. I suspect under the NY SAFE Act, the law in NY is the same. Also, some states have restrictions on ARs/AKs. For example, one cannot (currently) possess either in California unless it is equipped with a "bullet button." And don't even think of bringing in a machine gun without special permission.
There is one other important factor, touched on by a comment above. "No, officer, I don't consent to a search. Am I free to go?" The police cannot search a locked container without your consent or a search warrant-and refusing to consent to a search is NOT probable cause. Of course, if the police really want to search your car, they will keep at you to give consent, and try to keep you on the side of the road for as long as possible. I think that there is a recent case--Frank may know--that said that the detention cannot be indefinite, and I seem to recall reading that it may not exceed fifteen minutes, but I am pretty fuzzy about that.