Most dash cams come with a 12V power cord that you plug into your vehicle power source.
That said, if you want to hard wire it I think your best bet is the switched power wire that goes to the 12V vehicle socket you already have behind the radio. Pop the bezel, pull the radio (you won't have to unclip it) and look for the power wire.
On my Patriot, a 2011, it was a pinkish colour with a darker tracer...I think. Its been a long time since I was in there.
Just grab another person and a tester and make sure you have the right wire.
Also, most power cords for these small electronics are simply that, a 2 wire power cord so cutting it and hard wiring is fine but BEWARE if you have any sort of data that the camera uses that cord for. Some of the cords on some of them are the GPS antenna for instance.
