Out of Cairns there is only Green Island and Fitzroy Island that are classified as Outer Reef. Neither are great. Green can be quite expensive as you are have to get there via ferry, then book a dive around the fringing Reef.
Further north (close to Cooktown) is Lizard Island which will have the best access to the Northern Reef and Cod Hole, but again you have to fly there and is an expensive resort. Best diving of the Reef up there though.
Going south of Cairns you have quite a few to check out but you are moving away from the Outer Reef.
Lady Elliott (closest to Brisbane as classified as still being the GBR marine park zone), Heron Island (still 2 hours to get there though), Lady Musgrave and Great Keppel are the ones that still offer pretty good dives within the Marine Park. Magnetic Island is out of Townsville but its terrible diving from my experience with very low visibility and little marine life unless you get a boat ride away from the island itself.
Further north (close to Cooktown) is Lizard Island which will have the best access to the Northern Reef and Cod Hole, but again you have to fly there and is an expensive resort. Best diving of the Reef up there though.
Going south of Cairns you have quite a few to check out but you are moving away from the Outer Reef.
Lady Elliott (closest to Brisbane as classified as still being the GBR marine park zone), Heron Island (still 2 hours to get there though), Lady Musgrave and Great Keppel are the ones that still offer pretty good dives within the Marine Park. Magnetic Island is out of Townsville but its terrible diving from my experience with very low visibility and little marine life unless you get a boat ride away from the island itself.