Error when creating and connecting to Entity Framework database on an Azure virtual machine

A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible.

If your SQL Server instance is hosted on your local network, please make sure whether it has been configured that it can be remote access. If it can't be remote access, I am afraid you need to migrate your SQL Server database to your Virtual Machine or Azure SQL. Then you could modify your connection string to access the new database which can be accessed from your project.

I don't want to migrate anything, I want to make a new database on the VM..

You could use Local DB which works on your VM. If your application type is web application, you could modify your database as following. EF will create a new database in your App_Data folder.

Data Source=(LocalDB)\MSSQLLocalDB;AttachDbFilename=|DataDirectory|\Database1.mdf;Integrated Security=True

Otherwise, you need to put the detail configure the detail path of your database file in the connection string. For example,

Data Source=(LocalDB)\MSSQLLocalDB;AttachDbFilename=D:\Database1.mdf;Integrated Security=True

I just tested the LocalDB on Azure Windows 10 virtual machine with VS 2017 installed and it can create database when I use EF code first. Following is my test code.

class Program
{
    static void Main(string[] args)
    {
        using (SchoolContext context = new SchoolContext())
        {
            context.Students.Add(new Student { ID = 1, FirstMidName = "FMN", LastName = "LN", EnrollmentDate = DateTime.Now });
            context.SaveChanges();
        }

        Console.Write("Create database OK");
        Console.Read();
    }
}

public class Student
{
    public int ID { get; set; }
    public string LastName { get; set; }
    public string FirstMidName { get; set; }
    public DateTime EnrollmentDate { get; set; }
}

public class SchoolContext : DbContext
{

    public SchoolContext() : base(@"Data Source=(LocalDB)\MSSQLLocalDB;AttachDbFilename=C:\Users\amor\Desktop\TestEF\CodeFirstSample\Database1.mdf;Integrated Security=True")
    {
    }

    public DbSet<Student> Students { get; set; }
}