@vrain - unfortunately your satellite map link doesn't work here, so I'm guessing at the orientation and shape of your building. But from your description of facing west slightly south you should be able to see the direction of the tv towers at 317 degrees from a window, correct? These are really strong and LOS so you should be able to get a great signal from that direction.
The other direction at 150 degrees would be weaker (assuming the signals have to travel through significant portion of your building). These might require a bigger and better antenna to catch.
To clarfiy a little further, a simple antenna has the capability to pick up both analogue and digital but I will need a converter box to watch the digital channels?
yes - an antenna will pick up both digital and analog.
Also, I saw a converter box by RCA in Superstore yesterday that, if I remember correctly, said it had an antenna built in. Is this worth it or possible?
If the store has a return policy, then it's just your time that is wasted if it doesn't work. If the convertor box + antenna picks up all the stations you want then you're done! Otherwise just return it. It would give you a great idea of how well your reception is from your location.