Do you know the best place to place the connection string?

The best place to put the connection string is in the Web.Config file.That makes the code simple and easy to read. Look into the following code:

string cnnString = "data source=(local); integrated security=SSPI; persist security info=False; pooling=False; initial catalog=Northwind2";

and observe the following code which is simple and easy to read:

string cnnString = LinqToNorthwind.Properties.Settings.Default.NorthwindEFConnectionString;

private void Form1_Load(object sender, System.EventArgs e)
{
    //string connString = "data source=(local); integrated security=SSPI; persist security info=False; pooling=False; initial catalog=Northwind2";
    string cnnString = LinqToNorthwind.Properties.Settings.Default.NorthwindEFConnectionString;
    cboCity.Items.Add("London");
    cboCity.Items.Add("Madrid");
    cboCity.Items.Add("Sao Paulo");
    db = new NorthwindDataContext(cnnString);
    cboCity.SelectedIndex = 0;
}