I use Adobe After Effects CC 2017, and auto-save is turned on by default. The path of auto-save is marked as "Next to Project". My computer turned off yesterday, because of electricity. So where can I find my lost project?
Wherever you last saved your project.
I'm not sure whether or not After Effects will auto-save an untitled project..maybe it does.
Regardless, when you start a new project you always save it in it's own folder and name it.
Then you can keep any assets & project related files all in one place & autosave will have a project to "save next to".
If you screwed up or don't know what you're doing & were working on an "untitled project" you could try opening AE, hitting CTRL+ALT+N to start a new project, then immediately go (as you always should) to File>SaveAs & see what folder it defaults to. If there's something saved it might be there. Otherwise it might be in Documents\Adobe\AfterEffects (or whtever file path is greyed out in the autosave preference dialogue). You could also search your computer for ".aep" files.
After that....you're out of luck. Live & learn.
REMINDER: When you start a project always save it immediately with a unique name in a dedicated project folder. Then when auto-save, which is set to save "next to project", saves, there will be a "project" for it to save "next to".