You spawn right on the island.
This island is perfect: it has everything you need for a full Survival experience. It's just large enough to support a village on a plains biome, but it has a small forest biome for wood! Following a short cave from behind the Blacksmith's shop leads to a zombie dungeon that's almost above ground. Other features include an above ground lava pool, a short ravine with weird glitched floating water, and abandoned mines under the Southern Peninsula.
Tip: If you want other passive mobs such as cows, kill off the rest of the passives on the island (you can keep 2 of each for breeding.) This will trigger more spawns.