The least common site for a berry aneurysm is -
A berry aneurysm

The further away the aneurysm from the anterior circulation or from the circle of willis , the less common will be its rate of occurance.
Berry an aneurysm or Saccular aneurysm or Congenital aneurysm is the most frequent type of intracranial aneurysm.
Most aneurysms occur in the anterior circulation and are found near the branch points.
The most common site is junction between anterior cerebral artery and anterior communication artery (40%).
Next most common site is internal carotid artery and posterior communicating artery (20%)

Less frequent sites include -

Top of basilar artery
Junction of basilar artery and the superior cerebllar artery or anterior inferior cerebellar artery.
Junction of vertebral artery and posterior inferior cerebellar artery.
Vertebral artery
Basilar artery
Junction of anterior cerebral artery and internal carotid artery
Posterior cerebral artery