I need to create multiple Azure Function apps in different geographic locations over and over, so I need to automate this. Doing this in the Portal isn't going to scale. I thought there would be a Nuget package for doing this, but I haven't found it yet. Any ideas on how to automate the creation of Azure Function Apps?
There isn't an Azure Functions specific NuGet package or API. Functions works with the standard Azure Resource Manager APIs (consistent with the way you manage other Azure services) and new Function Apps can be provisioned using PowerShell, the Azure CLI, the ARM API or directly through the portal.
Under the "Get Started" section of the documentation I've linked to, you can find more information on how to create and manage templates.
I hope this helps!