The files are located here:
"C:\Program Files (x86)\Steam\steamapps\common\indiana jones and the last crusade\INDY3\savegame.___"
"C:\Users\<your username>\AppData\roaming\LucasArts\Indiana Jones and the Last Crusade\*.*"
I would be happy to post this info to Steam's support and the Steam forums instead, but because they for some moronic reason require separate accounts, I write about it here instead.