Poptropica's old islands can still be played in two different forms: the official Steam version of Poptropica, and an unofficial curation in Flashpoint.
If possible, please buy the Steam version of Poptropica to support the game. The Steam version does not contain every old island. Read its description in Steam to find out if your favorite islands are included.
Flashpoint can be used to play all of the old islands that are not available otherwise. Here's how:
Download the Flashpoint Infinity Download Installer from the Flashpoint Downloads page. (Flashpoint Ultimate can be used, but it requires much more storage space than Flashpoint Infinity does.)
Run the Flashpoint Infinity Download Installer. You do not need to change any of its default settings.
Launch Flashpoint.
Use the search bar to search for "Poptropica". Click the "Poptropica" result that appears.
Click the "Download" button to download the Poptropica curation.
Click the "Play" button to start the curation. Have fun!