While this is an ideal choice of making AIR desktop applications for those who does not want the Flex framework, I am still surprised that Adobe didn’t add this option to its new IDE product, Flash Builder 4.0. Flex/Flash Builder being the best AS 3.0 editor so far, this option is really missing.
There is a bug in the Adobe JIRA – https://bugs.adobe.com/jira/browse/FB-9303 . But honestly, this looks like a natural choice for Adobe (!?)
I was using a hack for making this work with Flex Builder 3.0 and same works for Flash Builder 4.0. Its is a simple method though:
In the Flex/Flash Builder IDE, select ‘New >> Project’ and select ‘Flex Project’ option.
From the Wizard, please select ‘Desktop Application (Runs on AIR)’, give a project name and click ‘Next’ button instead of your usual ‘Finish’ button.

The next screen prompts for defining the folder for debug. Leave it as is, unless you want to, and click on ‘Next’ button.
The next screen is where you have to do some magic. Here it is.
Change the file extension of ‘Main Application file’ from .mxml to .as — nothing else.

Now click your favourite ‘Finish’ button, and you are set. But, if you run your project, it doesnt show up; this is because the visibilty option of your native window is set to ‘false’ by default. So, open up your application XML file (That will be in the root and named ProjectName-app.xml), and uncomment the sub node of the node and set it to true. Here is how it will look like:

Now, you have your AS3 AIR project, and you have access to all the AIR API’s, and your ’stage’ attribute will have the AIR related properties.
Workaround, still works nice. Adobe, we need this option from the wizard.