Entity Framework DataContext classes have been found in a few projects' "Models" folders, however because this isn't truly a model, it doesn't seem appropriate.
The IDatabaseInitializer class and my DataContext are currently located at the root of my project, which annoys me as well.
Do I simply leave them at the root or a folder titled "Data" or something like, or is there a standard or recommended procedure for this?
Since the model is what preserves the state of your application, one might argue that it is the model. People placed it there for that reason.
It should go there if you're a good boy and employ an abstraction/repository layer.
Put it in the models folder if your Controllers are speaking to the EF context directly (a terrible idea). There is no reason to physically conceal anything that is not conceptually abstracted.
It is irrelevant. Due to the fact that all database-related files are stored in the Models folder, I placed it there.