I've read some dangerous advice in this thread. I'm a firearms instructor, and I've been working on an article covering this from an RV perspective. There is a lot of bad information out there.
First - do you have a concealed firearm permit in your home state?
If you don't, then you are generally limited to having a firearm unloaded and stored where the driver can't access it when in motion. When stopped, it's your domicile. Local laws will always apply, but MOST places will allow you to defend yourself in your domicile. You do have to deal with things like certain types of firearms being illegal in certain states, magazine capacity limits, etc.
If you do have a concealed firearm permit, then you enter a world with things like RECIPROCITY and RECOGNITION. Reciprocity is when two states have a formalized agreement to admit each others permits. Recognition is the same thing, but with no formal agreement.
My Utah permit - as a Utah Resident - is accepted in many states. It means that I don't have to disarm myself before crossing a border into a state where my permit is valid.
Some states only accept a permit held by a resident of the permit state. For example, if I'm a California resident and have a Utah permit, it won't be good in Florida. I also have a Nevada permit as a Utah resident. New Mexico will honor that one, even though they don't honor my Utah permit.
When carrying in a reciprocity/recognition situation, you are subject to LOCAL laws. They may be different from your home state. It is your responsibility to know them.
There is an app for smartphones called Legal Heat. I strongly recommend getting it. It has info on the laws of all 50 states.
There is also a book on Firearms Laws of all 50 States by Mitch Vilos. Get it. It's a good resource.