One of the ironies of the Bounty story is that Capt. Edwards on his way out to Tahiti, discovered (or rediscovered) Ducie Island, which lies 308 miles to the east of Pitcairn. When he left Ducie he set his course WNW, and passed within 100 some odd miles of Pitcairn. Had he set his course closer to the West, he surely would have spotted the island, weather permitting, and had he investigated, the Bounty story would have been very different. However, the mutineers on Pitcairn were well armed, and unlike the mutineers later taken at Tahiti, had no doubts of their fate if they were taken and were prepared to fight.
You may notice that this map differs considerably from others you have seen. They usually show them going north to Atafu, back to what is now American Somoa, then to Annamooka, then north to Wallis Island and on to the wreck. This map follows Edwards's own account, island by island. It was at American Somoa (now) that the Pandora became separated from the tender. Edwards, fearful for their safety should their small force arrive there alone, broke off the search and returned to Annamooka. After waiting some time for the tender, he returned north and resumed the search, as view Five of the map below shows.
The order of the islands may be difficult to follow from the labels it was: 1. Bora Bora and neighboring islands, 2. Aitutaki, 3. Palmerston, 4. Atafu, 5. Nukunono, 6. Savai'i, 7. Upolu, 8. Annamooka, 9. Tofoa, 10. Kao, 11. Manua, 12. Tutuila, 13. Upolu (again), 14. Vavau, 15. Toku, 16. Fonualei, 17. False sighting, 18. Tongatapu, 19. Annamooka (again), 20. Niuafo'ou.