User control of picturebox location

do you mean changing the location of the image in a picture box, e.g. specifying the image displayed is c:\temp\pic1.gif? or do you mean, the picture box should now be at a new location, e.g. 200 pixels from the top and 300 pixels from the left on the form?

I mean dragging it to a new location on the form.

You can use the mouse up/down.move events like below

private bool isDragging = false;
        private int currentX, currentY;
 
        private void Form1_Load(object sender, EventArgs e)
        {
            // load from some config file if needed for last set position
        }
        
        private void pictureBox1_MouseDown(object sender, MouseEventArgs e)
        {
            isDragging = true;
            currentX = e.X;
            currentY = e.Y;
        }
 
        private void pictureBox1_MouseMove(object sender, MouseEventArgs e)
        {
            if (isDragging)
            {
                this.pictureBox1.Top = this.pictureBox1.Top + (e.Y - currentY);
                this.pictureBox1.Left = this.pictureBox1.Left + (e.X - currentX);
            }
        }
 
        private void pictureBox1_MouseUp(object sender, MouseEventArgs e)
        {
            isDragging = false;
            // save the current values to some config file if needed
        }

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Thank You