Update 10.11.2018
If you do a complete re-install, including uninstalling prior versions of code installed on your machine the new version will be installed at
C:\Users\{UserName}\AppData\Local\Programs\Microsoft VS Code
Update 06.07.2018
Since Version 1.25 VS Code supports portable mode.
Instructions on how to use this are documented here.
You will need the ZIP file download version – not the installer.
After unzipping the contents of the archive, create a data folder inside the folder, where code.exe is located. All settings will now be saved there and can be brought along with you.
|- VSCode-win32-x64-1.25.0-insider
| |- Code.exe (or code executable)
| |- data
| |- ...
On macOS, the folder must be named code-portable-data and has to be a sibling of the app itself. Not inside the app.
|- Visual Studio Code.app
|- code-portable-data
The reasoning behind this can be read here: What is VSCode User Setup for Windows?
Update
If you are using the x64 version, the path is:
C:\Program Files\Microsoft VS Code\
C:\Program Files\Microsoft VS Code\Code.exe
Original answer
At this point and time (Version 1.19.2) Vs code no longer resides in your AppData folder, but under
C:\Program Files (x86)\Microsoft VS Code\
C:\Program Files (x86)\Microsoft VS Code\Code.exe