Mystic Island is a location from Pokemon Ruby and Sapphire. While it's very similar to Emerald in many ways, Mystic Island is a separate location that doesn't appear in Emerald.
If you're looking for a location in Emerald with a similar feel, perhaps you're thinking of Navel Rock. This island is home to the legendary Pokemon Latios and Latias, and can be accessed by defeating the Elite Four and becoming the Pokemon League Champion.