This works for ASP.NET MVC with Core 2

public void Configure(IApplicationBuilder app, IHostingEnvironment env)
{
// Use this code if you want the App_Data folder to be in wwwroot
//string baseDir = env.WebRootPath;

// Use this if you want App_Data off your project root folder
string baseDir = env.ContentRootPath;

AppDomain.CurrentDomain.SetData("DataDirectory", System.IO.Path.Combine(baseDir, "App_Data"));
}

Now you can put this code where you need it to get your App_Data folder

string dataDir = AppDomain.CurrentDomain.GetData("DataDirectory").ToString();

I think putting App_Data under wwwroot is a bad idea. With asp.net 5 when we publish/deploy we get 2 folders approot and wwwroot. Any files that are not going to be served by http requests should not live under wwwroot. It would be better for things that previously would go under App_Data folder to live somewhere under approot instead. This related question of how to access files from approot should be of help

The App_Data directory can still be used in ASP.NET 5, it just isn't created by default.

Create it under wwwroot. This is the path returned by AppDomain.CurrentDomain.GetData("DataDirectory").ToString()

If you want to use a different DataDirectory then you should call SetData:

  public Startup(IHostingEnvironment env, IApplicationEnvironment appEnv)
  {
     string baseDir = appEnv.ApplicationBasePath;
     AppDomain.CurrentDomain.SetData("DataDirectory", Path.Combine(baseDir, "myAppData"));