How can I open Windows Explorer to a certain directory from within a WPF app?

You can use System.Diagnostics.Process.Start.

Or use the WinApi directly with something like the following, which will launch explorer.exe. You can use the fourth parameter to ShellExecute to give it a starting directory.

public partial class Window1 : Window
{
    public Window1()
    {
        ShellExecute(IntPtr.Zero, "open", "explorer.exe", "", "", ShowCommands.SW_NORMAL);
        InitializeComponent();
    }

    public enum ShowCommands : int
    {
        SW_HIDE = 0,
        SW_SHOWNORMAL = 1,
        SW_NORMAL = 1,
        SW_SHOWMINIMIZED = 2,
        SW_SHOWMAXIMIZED = 3,
        SW_MAXIMIZE = 3,
        SW_SHOWNOACTIVATE = 4,
        SW_SHOW = 5,
        SW_MINIMIZE = 6,
        SW_SHOWMINNOACTIVE = 7,
        SW_SHOWNA = 8,
        SW_RESTORE = 9,
        SW_SHOWDEFAULT = 10,
        SW_FORCEMINIMIZE = 11,
        SW_MAX = 11
    }

    [DllImport("shell32.dll")]
    static extern IntPtr ShellExecute(
        IntPtr hwnd,
        string lpOperation,
        string lpFile,
        string lpParameters,
        string lpDirectory,
        ShowCommands nShowCmd);
}

The declarations come from the pinvoke.net website.