Can't find SDK folder inside Android studio path, and SDK manager not opening

If you have downloaded the AS + SDK bundle:

Assuming the defaults were left unchanged, you will find the SDK in C:\Users\%USERNAME%\AppData\Local\Android

If it is missing at this location, one of the following reasons apply: you have chosen a custom location, you missed to install the SDK at all, or (unlikely) they have changed the default install location.

Note #1: the AppData directory is hidden by default. If you have a standard Windows configuration, the C:\ path above should work "as is" (hit Win + R -> paste the path -> Enter).

Note #2: you will never find the SDK in the Android Studio directory unless you have explicitly put it in there. The reason is that those directories might be deleted after installing a newer version of Android Studio and you would have to re-install the SDK as well.

If you have retrieved the standalone SDK by some other means:

The SDK location may vary (from my experience), however (assuming the default configuration) you will most likely find it in C:\Program Files\Android or C:\Users\%USERNAME%

Tools > Android > SDK Manager > there you'll see the path to SDK

If you don't have it at C:\Users\%USERNAME%\AppData\Local\Android (this is where most people have it) than it is possible you don't have it installed. Go to Tools > Android > SDK Manager and then click on "Android SDK." On the top of the SDK Manager it will list the SDK Location. Click edit. If you don't have Android SDK installed, it will give you the option to install it in certain location. Install it, and Android Studio should work!