I've been dealing with this every year recently, traveling up the I-95 corridor and on to Vermont. It's not that bad when it comes to transporting...just don't expect to find a way to 'carry' while you are in the surrounding states.
You should look at the NRA's information on this topic.
NRA-ILA ::
This is the important part: US Code Title 18 Section 926A: "Notwithstanding any other provision of any law or any rule or regulation of a State or any political subdivision thereof, any person who is not otherwise prohibited by this chapter from transporting, shipping, or receiving a firearm shall be entitled to transport a firearm for any lawful purpose from any place where he may lawfully possess and carry such firearm to any other place where he may lawfully possess and carry such firearm if, during such transportation the firearm is unloaded, and neither the firearm nor any ammunition being transported is readily accessible or is directly accessible from the passenger compartment of such transporting vehicle: Provided, That in the case of a vehicle without a compartment separate from the driver’s compartment the firearm or ammunition shall be contained in a locked container other than the glove compartment or console."
As you can see, as long as you are allowed to have your firearm where you start from, and where you are going, and you properly secure the firearm, you may legally transport it through "unfriendly" jurisdictions.
I hope this answers your question.