Azure Web Site with SQL Server VM
As of October 2014, you cannot use an SQL Server hosted as a VM as a database server for an Azure Website. This is because Azure Websites do not support / cannot be a member of an Azure Virtual Network. Rats!
You will need to use a Azure Web Role instead.
This comprehensive-to-the-point-of-insanity post describes the differences in full: WINDOWS AZURE WEB SITES VS WEB ROLES