There's a lot of advice in this thread.
This is my procedure when I need to carefully research a trip.
1) Figure out where I have reciprocity. Obviously there are some websites that help with this but the best method is to check the attorney general's site for that state (or whatever entity handles their CCW permits) if there is anything unclear. If I have reciprocity then I cruise by HandGunlaw.us or check the actual state statutes to check out answers to key questions such as "do I have to honor gun-free-zone signs," "can I carry in rest stop areas," "do I have to show the cop my CCW permit" or "what about restaurant carry?"
1B) Check for stupid local laws like mag capacity bans and so on. Generally if you stay inside America you're fine. If you depart the country to places like NJ, NY, CA, etc then you need to doublecheck.
2) If I don't have reciprocity, check Open Carry laws. Open Carry.org has a useful map. Many states allow open carry without a permission slip. You just tuck in your shirt when you hit the state line and carry on.
3) If there is no reciprocity and no open carry, check Car Carry. For example, even SC with its relatively bad carry laws allows for people without a permission slip to carry in a car under certain conditions.
4) If there is no reciprocity, no open carry, and no car carry then I am pretty much down to traveling with the Federal FOPA shield. FOPA requires the guns to be unloaded and in a locked case inaccessible from the passenger area. You can make no non-essential stops. Think about driving and stopping for nothing but bathroom breaks, gas, and maybe a meal. Do not stay the night. Do not stop for a tourist destination. Do not do anything that could conceivably be considered as breaking your journey. I would suggest paying with untraceable cash as well if you do anything even remotely questionable like having a coffee with friends while passing through (not necessarily essential to the journey, is it?).
5) In all cases, prepare your vehicle. Remove junk and clutter. Empty cars attract less attention. Consider removing controversial bumper stickers, etc.
6) Prepare to exercise your 4A rights. Ask if you are free to go if stopped, and if not, then ask why not ("Officer, am I free to go?" "What crime do you suspect I have committed?"). Understand that you can and probably should decline a search. Understand that you should always decline a seizure ("I don't consent to your seizure of my property but I will not resist."). Have a tape recorder or recording app on your phone. Have a locking case inside the grabbable area of the car to put any possibly questionable items into; generally, anything in the grabbable area of the car (i.e. the entire passenger compartment) can be subjected to a "Terry Frisk" search with a pretty low hurdle for the cop to meet, but items in locked cases are entitled to additional protection against arbitrary and unreasonable searches.