In the US? It’s more about the state you are entering, rather than the one you are leaving. In general, you can buy a pistol in any state and take it to another as long as it is locked up and not loaded. If you have a conceal license, then things get different. Once it enters your car (in most states) it is considered concealed and does not allow you to open carry in your vehicle, which the constitution allows you to do anywhere but gun free zones (schools, banks).

Some states require you to register a pistol at purchase, others do not.