where does the ground wire on an aftermarket radio go to?

Attach the ground to any bare metal. The entire car body is ground.

If that black wire is a ground wire you don't wrap it around things...you either find another ground wire where it screws into the metal or you drill a hole in a metal support and screw the wire down with a metal screw.

On a good ground. You get a test light. Connect the test light to battery positive. Touch the ground point with the test light. Test light lights up, the ground is good.

Not any bare metal will do. If the bare metal is attached directly to the chassis of the car then yes, it will work as a ground.

There is always a chassis ground wire in the factory stereo connector, alternatively you can crimp a ring connector on the chassis bonding wire and ground it with a star washer anywhere you can find adequate chassis metal. Look at the factory connector and the adapter, several of the factory connector wires are not in the generic speaker wire adapter, like the antenna preamp power and the factory dash dimmer control wires.

Many of the newer cars may have a radio antenna preamp on the cars with combo XM/Onstar/satellite antennas, the blue acc amp pull on wire will then need to be connected to the proper factory connector wire.

RP; As said before, the new deck needs a star washer to chassis ground, it's not a floating ground unit.
It doesn't matter how the old deck was factory wired and ground bonded, info was for general purposes.