Lot's of Moose hunting around St. John's, but demand is high for close areas, so if you want a tag every year, you'll have to drive a ways, tags are by lottery/pool. Bears, as said, off the Avalon, at least 1.5 hrs, two per license, two licenses per year, spring and fall, so 4 max/year. Small game, other than the discharge ban, lots of good hunting in St. John's. I live in the city but can and do hunt small game legally in less than 8 minutes drive.
Woodland Caribou, closest herd within an hour, but not this year as the Avalon herd is closed. So now 2-3 hours. Not looking good for the caribou, which has inspired me to whack some bears this year, hopefully near to a caribou herd, bears eat young caribou.