The interesting and efficient way of deploying such static web site could be using only the blob storage and managing it from any of your favorite Azure Storage Explorer.
Below is a sample structure of one of the sample site blob structure uploaded and managed through Azure Storage Explorer.
Image : A Sample Blog Storage Structure for a Static Web Site
This approach makes it incredibly easy and quick way of deploying and managing a static web site on Windows Azure. Also, you could very well develop your complete site using your designer tools and any of your favorite HTML editors only.
If you are aware of the Windows Azure charges of consumption then you might have realized by now that this approach saves your dollars too. Yes! You don't have to provision a web role to run your web site; instead your site is running from the Azure blob storage itself and in turn saving charges required for running a web role.
You could very well create CNAME mapping to have your DNS name point to azure blob storage and make your site running from your own DNS name instead of an unfriendly URL like http://<account>.blob.core.windows.net/ .
Hope you agree this being an efficient way of deploying static web sites on Windows Azure.