By completing certain tasks, you can unlock additional areas around the island.

Area	How to unlock
Amusement Park	Have an islander confess his or her love.
Cafe	Have an islander confess his or her love.
Campground	Send a traveler from your island, or have a traveler visit and camp on your island.
Clothing Store	Have more than 1 male and 1 female islander, and solve 5 problems.
Compatibility Tester	Have 2 male and 2 female islanders, and solve 30 problems.
Concert Hall	Give a song to an islander who has leveled up.
Hat Shop	Have 2 male and 2 female islanders, and solve 10 problems.
Import Wear Shop	Communicate via StreetPass or receive an import item via SpotPass.
Interiors Shop	Save over $200.
Mii Homes	Celebrate an islander wedding.
Nintendo 3DS Image Share	Take a photo of a Mii's apartment using X or Y.
Observation Tower	Get a gift to an islander who has leveled up.
Park	Have an islander confess his or her love.
Pawn Shop	Get 5 different treasures.
Photo Studio	Have 10 or more islanders, and solve 50 problems.
Port	Activate StreetPass.
Rankings Board	Have 5 or more islanders and solve 15 problems.