Why doesn't Android appear in Eclipses' preferences?

Remove the plugin, then restart as follows:

eclipse -clean

Now try reinstalling the ADT from the online installation

OR

Head over to Help -> Install New Software. Click on Available software sites. Delete the Android repo. Uncheck Indigo & Eclipse updates & recheck them. Now head back to Help -> Check for updates. Once done, add the Android repo again. Accept the license & you should be good to go.

Happy Coding..

This won't fix your issue directly, but I suggest your take a look at the MOTODEV STUDIO for Android. Essentially, it's a customized Eclipse IDE with all the Android tools preinstalled and many more of their own tools for app validation. I find their tools usefull, especially the code snippets and the app validator. I believe you will need to register to download, but it's a quick and free process and you can always use a temporary email service. Anyway, this should allow you to get up and running until you find your bug (even if I don't see why you'd switch back to plain eclipse).

MOTODEV STUDIO for ANDROID

Check your plugins directory, located in the folder you extracted the original eclipse zip file to.

For me it is located in

eclipse-java-indigo-SR2-win32-x86_64\eclipse\plugins

and I see the following files related to the ADT plugin

com.android.ide.eclipse.adt_18.0.0.v201203301601-306762.jar
com.android.ide.eclipse.ddms_18.0.0.v201203301601-306762.jar
com.android.ide.eclipse.hierarchyviewer_18.0.0.v201203301601-306762.jar
com.android.ide.eclipse.traceview_18.0.0.v201203301601-306762.jar
overlay.com.android.ide.eclipse.adt.overlay_18.0.0.v201203301601-306762.jar

Make sure you have files similar to these.

Now open a shell and run the following in your eclipse install directory

eclipse.exe -console

you should get the osgi (Open Services Gateway Initiative) console. Now you can see whether your bundles have unresolved dependencies and start them manually. So try

osgi> diag com.android.ide.eclipse.adt

and

osgi> start com.android.ide.eclipse.adt

and check the output.