I'm originally from the Miramichi area. There are plenty of dive sites if you have access to a boat, but from shore, there are fewer. The two sites listed in previous post are acurate, dived both areas numerous times. The Petit-Rocher wharf site does actually go to depths of 70-80 feet if you don't mind the swim, excellent visibility and plenty of drop offs, but as stated in the link, it's a fair surface swim so a flotation device is highly recommended. I've done it many times with kayaks (which can be rented locally).
Tabusintac, Baie-du-Vin, Portage Island and Baie Ste-Anne all have nice sites, but a boat is required.