Where does my garage drain go and how can I unclog it?
Your garage drain could go anywhere--it could be tied into your septic system or sewer connection, or it could go to a separate exterior drywell or leach field. It could even head into a sump pit to be pumped out by a sump pump. Its impossible to know without a whole lot more information about your specific circumstance. 

As to how to unclog it, your best bet may be a high-pressure water jet snake.



These can be rented from tool rental outfits, or you could call in a professional. They tend to be better at removing sandy-type clogs than conventional drain snakes.