Android NDK Default location
The latest version extracts itself inside the current working directory. So if you launched it from the explorer, that's the same directory as your .exe.
You should find an android-ndk-rXXX
folder there. Otherwise that means it wasn't extracted.
It's always better to use the latest NDK, there are many bug fixes and improvements with each releases... You can open the .exe as an archive with 7zip, and extract it somewhere else if you need, or launch the .exe from a terminal set where you want to have it extracted.
I am using Visual Studio, but I also want to play with Android Studio. So, in order to get the Android SDK and NDK, I installed Android Studio.
The Answer
Android Studio installed the SDK naturally at
C:\Users\<UserName>\AppData\Local\Android\Sdk
The NDK folder is not yet ready, but is/will exist at
C:\Users\<UserName>\AppData\Local\Android\Sdk\ndk-bundle
In order to flush out the folder with the actual NDK, I had to tell Android Studio to install the NDK.
File -> Settings
Select Appearance and Behavior -> System Settings -> Android SDK
Click on the SDK Tools Tab
Checkbox the NDK (And, I think, the LLDB and CMake options).
Select Apply/Install.
Now that NDK folder should be good to go.
Android Studio 2.2 installs it in C:\Users\[username]\AppData\Local\Android\Sdk\ndk-bundle
(on Windows 10).