I worked in Bannockburn for a few months in '11 and spent some time pokin around in the Pisa Range and remember seeing plenty of hares on the roaring meg track and around the meg hut. I was just up for a tramp and I'm not sure if hunting is allowed there but the DoC site says there are opportunities to hunt in the Pisa Range so I'd give them a ring and find out where you could go.
Bookmarks