Well there weren't just pirates in the Caribbean during the so-called Golden Age of Piracy. If you're talking about pirates of European origin, they operated in the Atlantic, Pacific and Indian Oceans throughout this period.

The quick rundown is that throughout the 1680s and early 1690s, as European governments began cracking down on buccaneers in the Caribbean, many French and English buccaneers crossed into the Pacific (following the example of English privateers like Francis Drake and Thomas Cavendish who had done this a century earlier) and began attacking ships and raiding Spanish settlements along the Pacific coasts of South and Central America as far north as Mexico. These included Bartholomew Sharp, William Dampier, Basil Ringrose, Lionel Wafer, Raveneau de Lussan, Etienne de Montauban and many others who all wrote and published detailed journals describing their exploits which are a key primary source on buccaneers. After they finished plundering the Spanish on the Pacific coasts of the Americas, most of these buccaneers then sailed west across the Pacific and reached the East Indies. There they had problems dealing with local authorities and some became involved in local Philippine tribal conflicts. It took William Dampier over ten years to return to England like this, eventually completely his circumnavigation in 1691 and publishing his journals in 1697. He would go on to enter the Pacific and complete two more circumnavigations as a legal privateer against the Spanish in 1704-1707 and 1708-1711.

In the 1690s, as buccaneers in the Caribbean continued to be persecuted, another wave of English and French pirates sailed for the Atlantic and Indian Oceans to get away from European authorities. This era is commonly called the "Pirate Round." These included most famously Thomas Tew who was killed in battle against a Mughal ship in the Red Sea in 1695. There were some rumors that these Indian Ocean pirates founded some sort of proto-socialist/anarchist "pirate utopia" in Madagascar called Libertatia, but this is probably an invention of the author of the book A General History of the Robberies and Murders of the Most Notorious Pyrates published in 1726. In reality, the pirates in Madagascar probably didn't do much more than establish a few trading posts and maybe participate in some tribal conflicts (a future ruler of Madagascar, Ratsimilaho, was said to be the son of Thomas Tew via a Malagasy queen). In 1695, the pirate Henry Avery captured an extremely wealthy Mughal ship in the Indian Ocean and this caused a huge international scandal in which British East India Company officials were imprisoned by the Mughals in India and the English government was forced to issue a proclamation unequivocally condemning piracy, labelling pirates hostis humani generis meaning enemies of mankind. Henry Avery escaped with his loot and was never heard from again, but because of this, British pirate hunters were organized to try to stamp out piracy in the Indian Ocean. One of these named William Kidd turned pirate himself after an extremely unsuccessful two year voyage from 1696 to 1698 in which he failed to encounter a single pirate in the Indian Ocean. He was tried and executed in 1701.

Throughout the 1700s and 1710s, many English privateers crossed into the Pacific again to attack the Spanish but these were more technically acting as legitimate privateers since they did it with valid privateering commissions during the Spanish War of Succession between England and Spain.

After the Spanish War of Succession ended in 1713, many of these former privateers who had established themselves on the island of Nassau in the Bahamas as a base for their activities, continued attacking ships despite the war being over -- this made them pirates. Around the time Nassau was invaded and taken over by the British government in 1718, many of these pirates fled the Caribbean like the earlier generation of pirates had in the 1690s. Also like in the 1690s, there is some evidence of some small pirate kingdoms or fiefdoms being set up in Madagascar, most notably under the pirate James Plantain until 1728. The pirate Edward England sailed for the coast of West Africa in 1717 and ended up being marooned in the Indian Ocean in 1720, eventually making his way to Madagascar where he died. His most powerful successor, Bartholomew Roberts, was killed by pirate hunters off the west coast of Africa in 1722.

Other pirates like Edward Thache (Blackbeard) sailed for the North American colonies where he briefly settled in Charles Town, North Carolina, and made deals with the corrupt local governor, but he was killed by pirate hunters in 1718. Other pirates like Edward Low and John Philips continued attacking ships along the coast of New England throughout the early 1720s. One of the last New England pirates was William Fly who was hung in Boston in 1726.

In Europe, the Scottish pirate John Gow briefly terrorized the coast of Scotland from 1724-1725 before he was captured and hung and a few Irish pirates Philip Roche and Walter Kennedy also briefly engaged in some small-scale piracy around Ireland and Scotland before they were captured and hung in 1721 and 1723.

Sources:

A General History of the Robberies and Murders of the Most Notorious Pyrates published in 1724/26 by Charles Johnson/Daniel Defoe/Nathaniel Mist (Charles Johnson is a pseudonym, long thought to have been written by Defore but Mist is the most likely author)

Pirates: Terror on the high seas from the Caribbean to the South China Sea by David Cordingly et al.

The Golden Book of Buccaneers by John Gilbert