Elves:
Grey and High Elves: They’re city dwellers, so distilling wouldn’t be unknown, but I still don’t see them as whiskey drinkers – probably wines and some brandy predominately.
Drow: being decadent sorts would enjoy anything – preferably ‘acquired’ in raids, or made by lower caste drow. Distilling underground would have some challenges, but nothing too extreme – the main problem is availability of ingredients. Everything I can find tells me that fungi (aside from yeast, obviously) aren’t useful in distilling, so the hypothetical mushroom beer of the drow and dwarves is probably -flavored- with mushrooms, but still has some sort of a grain base.
Wood elves and Grugach – The idea of grugach hicks out in the middle of nowhere defending their stills from ‘dem nosy outsiders’ has momentary appeal, but not in a serious campaign. If they’re nomadic or semi-nomadic, they could concievably carry around leather skins of still-fermenting beverages, similar to the way the mongol’s made their kumiss.
Sea elves – No fire, so no whiskeys, and how exactly would you keep your drinks from just, er, diluting out into the water around you? Basically, the sea elves are (ironically) dry.
