Yeah, you go to islands to get other fruit. All the islands have coconuts on the beach and are usually mini versions of your island (so they have the same native fruit as you). A rare island will be full of tarantulas (which sell for like 8,000 bells and you have to dig holes in a box shape to catch them and jump over the other side so they don't bite you), have bamboo only, or have non-native fruit. I explain in this post how to increase your chances of getting a rare island:
Animal Crossing: New Horizons Discussion
If you have the Nintendo subscription, you can visit other people's islands in order to get their fruit, though. (I ain't paying for that, though.)