Where does homebrew install the android-sdk when you run the command:
brew cask install android-sdk
I want to be able to add it to the PATH
You would be better off using the symlink that Homebrew creates to ANDROID_HOME, as it will always be the newest version:
/usr/local/opt/android-sdk/
So your PATH would be:
export PATH=$PATH:/usr/local/opt/android-sdk/tools:/usr/local/opt/android-sdk/platform-tools