I need an advice how to achieve the following functionality under Android:
According to android help, "drawing to a View, is your best choice when you want to draw simple graphics that do not need to change dynamically and are not part of a performance-intensive game." This is the right way to go when making a snake or a chess game, for instance. So I don't see a point in suggesting using a SurfaceView for this, it will just overcomplicate things.
For clickable areas you override public boolean onTouchEvent(MotionEvent event) where you manage x and y coordinates of the click for identifying the clicked area.