Let's assume I had an 80% firearm lower and wanted to complete it into a finished firearm myself.

This is illegal in NJ as a non-FFL individual (illegal to manufacture firearms, even if for personal use).

However, if the finished firearm is not illegal to possess in NJ then conceivably I could finish the lower in another state where personal manufacture is legal and then transport back to NJ, all legally.

Which states nearby to NJ could I legally finish the lower in and then legally transport the finished firearm lower (either long gun or hand gun) back to NJ?

I think Pennsylvania is strict on transporting handguns in cars without a concealed permit.  

What about Delaware? Connecticut?  New Hampshire? Vermont? West Virginia?

PA is fine for transporting a handgun in a vehicle.  Without any permit, yes - you are limited as to where you can go.  But transporting from a place of repair back home is fine.  Also, you are legal to transport a handgun anywhere, for any (lawful) purpose, in a vehicle, if you have any other state's permit (Utah, for example).

Man this state sucks.

Looks like he's waiting for the great Stromboli in the sky to land on him.