Islands I keep going back to

Faroe Islands

North Atlantic en.wikipedia.org

Hire a car. The tunnels between islands are an experience in themselves.

Hydra

Saronic Islands, Greece en.wikipedia.org

No cars. Donkeys and water taxis only.

Naoshima

Kagawa, Japan en.wikipedia.org

Hire a bike and spend a full day at the art museums.

Vis

Dalmatia, Croatia en.wikipedia.org

Menorca

Balearic Islands, Spain en.wikipedia.org

Quieter than Mallorca and the coves are better.

Lofoten

Nordland, Norway en.wikipedia.org

Azores

Portugal en.wikipedia.org

São Miguel for the hot springs, Pico if you want to climb something.

Isle of Skye

Scotland en.wikipedia.org

Madeira

Portugal en.wikipedia.org

Zanzibar

Tanzania en.wikipedia.org