when using InStr function, it fills the target cell repeating info

You're retriggering the change event when you change the cell in the event code. Not sure what logic you want, but maybe this:

Private Sub Worksheet_Change(ByVal Target As Range)
    Application.EnableEvents = False
    With Target
        If .Column = 1 And InStr(.Value, "to be opened") > 0 Then
            .Offset(, 1).Interior.ColorIndex = 45
            .Value = .Value & Format(Now, " yyyy-mmdd hh:mm")
            .Interior.ColorIndex = xlColorIndexNone
        End If
    End With
    Application.EnableEvents = True
End Sub