If what you say about the SDK Manager in the OP is correct, and if you have access to the SDK Manager, then it shows where the SDK is currently located.
Right below the Package and Tools menu, it shows the SDK path.
However, if you cannot access the SDK Manager, then odds are you downloaded either the ADT Bundle or the SDK Installer.
If it is the earlier, then the file that you downloaded is named: adt-bundle-windows-x86.zip. If it is the later, and if you remember installing it, then the default path for the installation is in your Program Files\Android..... The installer is named something like this: installer_r21.1-windows.exe (this is the current available version)
If none of the suggestions on this page, helps, then the last resort is to download the SDK all over again. On a good connection, you should be done in about 15 odd minutes.
Download Source
Good luck with coding. ;-)
