"gonna" is not a contracted form, it is slang. It is slang for "going to VERB". You can't use it to mean "going to PLACE". I am gonna eat all my dinner = I am going to eat all my dinner. I am gonna go to Long Island = I am going to go to Long Island. Your two examples are both incorrect. I'm gonna to Long Island = I'm going to to Long Island. <--- incorrect I'm gonna Long Island = I'm going to (VERB) Long Island. <--- incorrect. "gonna" will always have another verb after it. It cannot mean "to go" by itself.

You can use gonna if you right it like this: I'm gonna go to Long Island. Gonna sounds less professional though.