"I don't drink" is almost always good enough by itself. My best friend doesn't drink and I have rarely seen it questioned beyond that; "Medical reasons" is usually all the elaboration necessary.

There's an old trick of getting a nonalcoholic drink that looks like an alcoholic one. Ginger ale in a short glass looks like scotch & soda. The gibson (a martini with a cocktail onion) was actually invented by a guy who was sick of drinking at social functions and just put water in a martini glass, and garnished his drink with an onion instead of the typical olive so that he could recognize it.