Can I get all the fruit types by visiting Random Islands?

Solution 1:

No, unfortunately you'll not be able to get all 6 fruit types without using online services. Currently, the game will let you get only 4 different fruits with local play:

1. Your native fruit
2. The fruit your mom sent via e-mail
3. Coconuts on mystery islands (using Nook-Miles Tickets)
4. Your sister fruit on the Sister Fruit Mystery Island

PS: It's not possible to know which is your sister fruit until you visit the island for the first time. But then, when you visit this same island again, it will always be the same sister fruit you found the first time.

PS²: There are rumours you can receive different fruit from villagers as a mail gift, but I personally never experienced this.