Sadly you can't. You have to become a member to access those parts of the island.
Chat with our AI personalities
Paid Moshi Members can shake the Rox trees at the Port to get free Rox.
Get a code
If you are a paid Moshi Member, you can change your monster's color at the Colorama shop in the Port. The only way to change to a different monster is to get a new Moshi Monsters account.
Go to moshimonsters.com and adopt a monster. Follow the steps for either a free Basic membership or a paid Moshi Membership. Once you have completed the steps to register, wait for an email from Moshi Monsters. There will be a link in the email that you need to click on to activate your Moshi Monster account. You will not be able to access your Moshi Monster account until you have completed the activation step.
A Moshi is what the monsters are called: "Moshi Monsters". You can not catch a Moshi Monster, you adopt a Moshi Monster when you start your Moshi Monsters account. Choose carefully as you can not change your Moshi Monster once you have verified the account.