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Rockhopper Island is the place where Rockhopper resides. It is known to be sandy, and filled with red puffles. There is a huge cave named Rockhopper Cave where Rockhopper stores his treasures. Many Penguins think that they could access Rockhopper Island in the future. This island is rumored to be VERY far away from Club Penguin Island. You need to cross several islands to get there, mentioned by the book, The Journal of Captain Rockhopper. Issue 2 of the Club Penguin Magazine says Rockhopper Island is about a month's sailing away from .
Club Penguin Island
When penguins completed the adventure in Rockhopper's Quest, there was a tear at the top of the map, which could have possibly been where Rockhopper Island was shown.
Currently, it is impossible to go to Rockhopper Island.
Rockhopper Island is rumored to be east of Club Penguin Island, according to a drawing in the lighthouse.
Many penguins thought that when the Rockhopper's Quest party started on Club Penguin, Rockhopper Island would be accessible. However, this is false after the Club Penguin Team confirmed that Rockhopper Island won't make an appearance, and denied the island's appearance again in the Club Penguin Times.
The island is mentioned in the Penguin Band's song
Anchors Aweigh. Rockhopper Island is a tropical and a volcanic island.
Rockhopper in Club Penguin Times stated that there is a restaurant on Rockhopper Island which is closed on Thursdays.
It could be possible that penguins can access Rockhopper's Island in the near coming future.
According to Polo Field, Rockhopper Island will be visitable "one day."
 Rockhopper once classified that there is a stinky cheese shop in Rockhopper Island and that shop is closed on Thursdays.
Spike Hike asked on Twitter "What do you guys think is on Rockhopper Island?", giving an indication that we may soon be able to travel to Rockhopper Island.
On Issue #412 of the Club Penguin Times, Rockhopper said that there were lots of "Stinky Cheese Trees" in the island.
This is nature habitat of red puffles.
Rockhopper's Ship/The Migrator
Rockhopper's Ship is here before Rockhopper and Yarr come to Club Penguin, which is usually during a big party or event, and is announced in the newspaper most of the time. Rockhopper gives Non-Member and Member items, at the shop in his ship, The Migrator, which can be found at the Beach, but only when Rockhopper is around. Also, there is a map from Club Penguin Island to Rockhopper Island.
Rockhopper Island's Known Locations
Rockhopper Cave (The Place where Rockhopper stores his treasure).
Unknown Room (An unnamed room in Rockhopper Island, there is a picture above but it is unknown where it is, or if it ever will be seen).
Rockhopper Jungle (A Jungle in Rockhopper Island, there is a picture of this above but it could've been just a beach).
Rockhopper Tiki (A pool with a Tiki entrance)
Rockhopper's Journal is in the Book Room, which can be found upstairs in the Coffee Shop, located in The Town, there is a book on Rockhopper Island.
Rockhopper Beach (A beach on Rockhopper Island, shown above).
Yarr The Red Puffle
Closest assumption as to where Rockhopper Island is located.
Possibly Rockhopper Island or Innocent Island.
In the animated short "Captain Rockhopper vs. Mighty Squid", the Squid barfs out Yarr and other items including a map. It's possibly the map of Rockhopper Island as there are palm trees seen on the map.
Possibly Rockhopper Island.
Plausible theory of where Rockhopper Island is located (click for full size).
Sources and References