Be very careful that it is legal to carry/transport/own/etc that firearm at your destination!
For example, New York. Don't bring one there. (I appreciate the tips from other HNers in that regard, I had no idea.) I'm not sure exactly what it is that is illegal in NY, in fact -- is it specifically airport related, or is it general ownership/carry/transport?
Theoretically there is a federal protection for possessing an unloaded weapon locked in a case (with the ammunition in a separate locked case), provided that you are simply passing through a place where it would be illegal (e.g. flying from Seattle through NYC to Vermont, for instance) but the local respect for that protection may vary. New Jersey, for instance, completely ignores it (you will get arrested and charged, but that works as a defense to the charge).
As in, you won't get one without political pull. There are 50-60 thousand currently outstanding, in a city of 8 million. Long gun possession licenses are similarly restricted, or at least roughly as rare.
The Firearms Owner's Protection Act of '86 protections for interstate travel are pretty much written with car travel in mind, and you can't really observe all of them while carrying guns in luggage. And it was always an affirmative defense (something you could only bring up while at court), but indeed New Jersey was particularly obnoxious about it.
And there's a big problem if there's any chance your plane will be diverted to "denied territory" as I like to call it: if the system doesn't put your bags in another plane but demands you take possession of them until you can get a flight or whatever, you're screwed if you have to continue by plane. When you go to the counter to check in again, and declare your gun(s), surprise! you aren't legally possessing them. I don't see much choice but to never take possession, or use some less searched method of ground or rail transportation to get back to the real USA while crossing your fingers.