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.
Why default your program would be installed here..
C:\Program Files\Microsoft VS Code\
If you have chosen different directory while installing it you can get it by:
1. Go to the icon location
2. Right click open properties
3. Check target
The difference is: System Installer will install VSC in C:\Program Files\Microsoft VS Code\ User Installer will install VSC in %HOMEPATH%\AppData\Local\Programs\Microsoft VS Code\
Search for the files with respect the version installed.