Great Harbor is the next harbor to the east from Little Harbor. It's quite a bit bigger and offers a handful of moorings in addition to good anchoring along the eastern shore.
Great Harbor is a wide-open and deep harbor making for a very easy approach. As you enter past Great Harbor Point, you will see some ship's moorings in the outer area of the harbor.
If you are looking to anchor, your best bet will be close along the eastern shore, even still you may find yourself in 30'-35' of water. The center of the Harbor is up to 80' deep making it excellent for those ships moorings but too deep for anchoring.
If you are looking for a mooring, you will find a small mooring field along the western side of Great Harbor. There is some good snorkeling along the reef from these moorings and in front of the beach club you will likely see some big rays. Ashore you will find a great little beach club called the Ocean's Seven. It's a recently refurbished establishment that serves drinks, lunch and dinner. They are open 7 days a week and have a happy hour every afternoon. Ocean's Seven can be hailed VHF 16.
You can access Sprat Bay, the Peter Island Hotel and yacht harbour and Deadman's Bay on foot from Great Harbor if you dinghy ashore on the south eastern side of Great harbor. From there is just a short walk east.