tl;dr: OP, yes, you may legally transport your firearms to a friend's house in PA to plink with friends.
Long version:
The laws that MDX linked are your best resource. Here is a summary regarding the OP's question and the subsequent licensing questions that were brought up:
1) Any person allowed by law to own a firearm may openly carry a loaded firearm on foot in the state of PA, excluding cities "of the first class" (> 1 million residents, so currently this applies only to Philadelphia). Note: ON FOOT. You cannot drive somewhere while OCing unless you qualify for an exception (next bullet).
2) If a person has a PA LTCF, or a concealed carry license from any other state, they may "openly carry" in the vehicle.
What I am saying here, OP, is that you may openly carry a firearm in PA except in Philly, and since you have a NYS pistol permit, you may also drive to your destination with the firearm on your hip. The following does not apply to you since you have a NYS permit, but I want to be clear about one thing: it is illegal for a person who does not qualify for an exception to transport their weapon, locked up/in the trunk/etc, then take it out when they arrive at their destination so that they may OC the firearm. This portion of the law is dependent on intent - if you are going to a shooting range, or going to some hunting lands, what I described is legal. But if an unlicensed or otherwise unexempted person is going to the grocery store, they cannot lock up their handgun in the trunk, drive to the store, then OC the handgun at the store.
I know that's a bit confusing. OP, given your current licensing status, you may carry openly in all of PA except Philadelphia, and you may carry in your vehicle.
Regarding Licensing:
1) Non-residents may apply to any PA county of their choosing. You do not have to apply to a bordering county.
2) PA law currently requires that the picture on your license is in their system. They currently have only one way to do this, and that is to take your picture while you're in the office. This is the only reason we are currently required to apply in person. There is no law requiring that we apply in person, only a technical hurdle that no county has passed (yet). Note that this is a new requirement as of about a year ago, so you will find people who have LTCFs but did not have to apply in person.
Again, I am providing a high level summary of my understanding of the law. While I am highly confident in my understanding of the law, the laws themselves are your best resource.
