Would it be semantically correct for me to say I went to the ocean if I'm referring to the Gulf of Mexico?

Well it is connected to the ocean. But then again, all the oceans are connected. I’d say that you could get away with calling it part of the ocean.

you could just say you went ‘to the beach’.

or, better yet, “to the gulf.’

Eww! Don’t go in that water!

Maybe you could say you went to the Caribbean. Let other people figure out if it’s the ocean. They can ask us if they’re not sure.

Is there an actual line where the gulf stops and the Atlantic begins?

@tinyfaery, as someone who grew up on the eastern seaboard, I agree with you wholeheartedly for the area around Galveston, TX. Padre Island, OTOH, ain’t so bad. South of Tampa/St. Pete is pretty, but watch out for the stingrays.

The Gulf of Mexico is considered a part of the Atlantic Ocean, so I guess it would be correct to say you went to the ocean.
As for a cut-off point. There isn’t really. The Gulf stream reaches all the way back home thanks to the North Atlantic Current