Im putting up drywall in my basement. Two of my walls are exterior
walls and my studs are about 6 inches from the wall. Should I put
up plastic as a moisture barrier before putting up the drywall. Im
not installing any type of insulation.

Even a plastic sheet directly over the concrete wall will form
condensation between sheet and wall and eventually smell moldy.

Good point!

The best place for any membrane though is outside
the wall underground befor backfilling.

Yep, that was my thinking too, but I didn't get the impression that was an
option in this case.

Anthony