Generally the one across the fence is always greener anyway, so get two islands close enough to cross between, and build a fence between them.
It should have plenty of coconuts, if you catch me, that you can eat with your banana. Also, take an island with mountains, because everyone want to get on top of an island, you can see some beautiful things from up there! A mountain with a large whole or cave is great for sticking your things in. You may sweat a lot on this island, but who cares, that island is hot.