Android Studio Not Including SDK
Go to the SDK Manager and click Edit... next to the field for the location of the SDK. Then an "SDK Setup" window should display. There you can download the SDK.
Edit: This answer is deprecated as Android Studio seems to bundle everything since a while already.
Old answer
It seems the android-studio-bundle version is no longer available in the download page (instead there are only android-studio-ide). When you start Android Studio, it won't let you create a new projet until you configure the SDK location.
That means you have to download the SDK separately here, extract it somewhere, and configure it on Configure->Project Defaults->Project Structure. After that, the SDK Manager icon will be enabled and you can download the tools you want.
