To begin with, there is one overriding principle that needs to be taken into account if you are traveling to any particular location and plan to bring a firearm: know the laws in that location. Also, know the laws in any locations that you will travel through if you are traveling by vehicle as any state or city ordinance applies to you when you cross through that area. With that said, what follows is some advice for traveling armed and it goes on the presumption that you are aware of the legal aspects of the vicinities in which you will pass through or reside.
Travel by Vehicle
If you are planning to travel somewhere by vehicle, perhaps on vacation or to visit family within the United States and you wish to bring your firearm(s) for self-defense, know the law as it applies to the ownership, carry, and transport of said firearms in that location as well as any others that you will travel to or through. If you are traveling to a gun friendly location that honors your carry permit you may be good to go and legally able to carry your gun in that location, but you may need to pass through territories where your carry permit is not valid. If that is the case, you many need to keep your firearm(s) unloaded and in lockable cases in the trunk of the vehicle. Typically you also need to keep all magazines unloaded and ammunition stored separately as well.
If that sounds ridiculous then I am sorry to break that cruel reality to you. Such states or jurisdictions that require this apparently want to make sure that only criminals carry guns and that law abiding citizens can’t defend themselves. That, however, is the reality in many places at the time of this writing. The nation needs national reciprocity for all carry permits, but we have many politicians that wish to do away with all firearm ownership, let alone grant national reciprocity. If you are a gun owner and value your freedom be sure to be politically active on this issue so that we can restore our Second Amendment rights everywhere in the nation. Until that happens, know the laws when driving.
If you are legally able to wear your gun or have it in the vehicle with you on your road trip then spend some time considering the safety of that weapon while on your trip. It is my opinion that when traveling in a vehicle the best place for a defensive handgun remains the same as it is in any environment: being on your person. Many people will remove the gun from their hip or wherever it is usually carried and put it in a center console or other vehicle compartment. The problem with this is in a time of crisis you very well may reach for the gun in its usual location only to realize that it is in the glove compartment. If you perhaps keep a firearm in a dedicated vehicle location in your daily life, perhaps on your daily commute, then obviously the firearm may be in a familiar location, but consistency is important.
Another vehicle issue with many is the security of the weapon from unauthorized access. A top priority for any gun owner needs to be the insurance that the weapon does not fall into unauthorized hands, most notably children. I am personally not a fan of handguns in glove compartments. This is because these guns typically get left in the glove compartment more frequently than anticipated. All it takes is for an unattended child to be in the vehicle and perhaps stray into the front seat and become curious, as all children will do if they gain the opportunity. If the child finds that gun you could have a tragedy unfold. I am simply a proponent of carrying your handgun on you, especially if in proximity with children, and if it is not on you it should be in a container that locks. If you keep a handgun in a glove compartment lock it when not in the vehicle.
If you wish to carry your firearm in a vehicle compartment that is locked but still quickly accessible consider using a quick access safe or other locking mechanism that you can mount in your vehicle. The added benefit to this, of course, is that the firearm will be locked up and less prone to walk away in the event of theft. Guns, when left in a vehicle that is unattended, even for a short period of time, need to be locked up. That may not be convenient, but it is necessary. Similarly, if you keep a dedicated long gun in a vehicle whether daily or on a road trip, that gun needs to be locked up in some fashion. A rifle or shotgun simply rolling around in the trunk is irresponsible and you can inadvertently arm a criminal who happens to break into your vehicle. Guns in cars need to be locked, period.
Travel by Airline
If you are traveling by air to a location that honors your Second Amendment rights you can usually transport a handgun as long as you declare the gun in checked-in baggage. Be sure to check both the current TSA regulations and the regulations and policies of the individual airline that you are using to ensure that you know the particulars of how to package and declare the firearm. Generally, at the time of this writing, you can lock an unloaded firearm in a lockable hard case within a checked bag. The ammunition must be separate from the gun and all magazines must be unloaded. You need to tell the airline employees that you are declaring a firearm and there is usually a form that has to be signed.
I will not delve into further detail as you must be sure to fully investigate the requirements yourself as they do change on occasion, and even based on airline or location. As long as you travel to a location that allows you to be armed with a handgun, and that honors your permit if you will carry it there upon arrival, transporting your firearm via air travel is usually possible. Be absolutely sure that you do not carry any firearm, ammunition, or other weapon with you into the airport or try to go through security with it or you will end up getting arrested. A firearm must be declared and must be locked away only in checked baggage.
One thing I suggest if traveling by airline is to keep your weapon needs as simple as possible. Each handgun that you transport needs to be locked in a container, the ammo needs to be stored separately, and magazines need to be unloaded, so it can get complex. My preferred gun when I travel by air is actually a small revolver. This is because the revolver does not need magazines and upon reaching my destination the revolver is easy and fast to load and secure on my body, rather than loading magazines. A small revolver, a couple speed strips, and a box of ammo makes a convenient travel companion. Obviously if you don’t like to carry revolvers you will need to load some magazines upon arrival to your destination, but streamlining your carry gear to only what you need can make your travel easier.
Safety at your Destination
When you arrive to your destination you must maintain proper safety and security with your firearm just as you would at home. If you are staying in a house with relatives or in a hotel room, be mindful of security as it pertains to your own family members or children, or perhaps the children of anyone you will be spending time with. A lot of people who do not have children of their own become careless with leaving firearms lying about and do not consider the ramifications of visiting children, or even irresponsible adults.
The simplest solution for maintaining security of your handgun is my favored approach: I wear my handgun from the moment I wake in the morning until the moment I change and go to bed, unless I am in a place where I can’t legally carry. If you want to be armed while you are somewhere away from home, then the only way to feasibly do that safely is to have the gun on you. But even if you do carry all day, every day, you do need to secure the firearm at least at night when you sleep. When I travel I always bring with me a small and portable quick access handgun safe. When I go to bed the little safe sits next to me on the night stand and this ensures my handgun is secured.
If you want a gun with you in a hotel room and you will not carry it all the time then having such a portable quick-access safe is the only responsible way to do it. Also, if you are on vacation, perhaps at the beach, if you plan to swim then obviously you may need to secure your gun at some point. A safe is the only way to do that responsibly. The handgun should be on your person or locked up. This should be the overriding principle when at home or away from home.
With some planning and responsible gear selection you can ensure safe and legal travel to your destination, and safe carry and storage of your firearm while at that location. I think bringing a firearm with you when you can legally do so makes good sense, but you need to do so responsibly. If you are willing to invest the effort into responsible transport and carry, being armed and prepared so that you can take care of yourself and your family will make your trip that much more pleasant.