i was asking my self the same question and wasnt getting good results on the web. here is what i gathered.
fire salts: skyrim 3x in septimus signus outpost. Directly North of college of Winterhold. 2-4x in fellglow keep by killing the fire atronachs (firey females from hell) throughout the level but especially when facing the boss who is called "the caller" who summons them. (dont kill the caller until you get a good amount of fire salts.) 1x in Arcadia's cauldron from the shop owner 1x in the arch mage's quarters. (you only can get into his quarters after you complete the "under saarthal" quest) the rest were random run in's with fire atronachs.
hope this helps. i wish i had had this. -c0ng0tr0n