For Mirimachi, the trails at French Fort Cove are awesome. French Fort Cove is very easy to find, has a good sized parking lot at the trailhead with some maps posted I believe. Otherwise, drop in to Incline Sports and chat with Scott, he’ll tell you the best way to ride the trails.
For Moncton get a hold of Dwayne Beaumont...firstname.lastname@example.org. He is one of the lead guys in taking care of the absolutely awesome trails at HIllsborough.
Kouchibouguac has some trails in the park. Won’t blow your mind from what I’m told, mostly gravel path, but it’s still a ride.
For Bathurst, you aren’t too far away from Campbellton (Sugarloaf) for some DH, lift access if it’s still open then. Check out their site at parcsugarloafpark.ca/bikepark/.
Shediac, I’ve heard there is mostly ATV trails, but haven’t personally ridden much around there.