So, I had this happen to me today, and was wondering what I should have done.

I teed off, and hit the green in one shot... problem is, it was the green of the hole beside me. Obviously I'm not going to take an iron and go and hit my ball off a green... so what should I have done?

I ended up just hitting another and going and picking up the first ball on the way up the fairway. I wasn't going to risk the (good) chance of me wrecking up a green...

But if this were to happen in an official USGA rules governed game... what should have been done?

Good call on not playing that, its a 2 stroke penalty if you hit it from the green.
Official ruling is to take relief one club length from the edge of the green, no closer to the hole you're on. But due to etiquette for casual play, if someones waiting to hit up to that green I'd take relief at a much safer distance away from the green. Or wait until after they've hit their approach shots.

Cool, thanks!