To get from the Westin (aahh nice!) to the Observatory (very nice!) have a look at the
Westin Map. Zoom out the map, and the Observatory is just off the top left of the map. It would be about a 20 minute walk - I suggest head north (towards the Harbour Bridge) on George, left (west) onto Margaret, then right (north) onto Kent Street. Your concierge may suggest going through Wynyard station.
The Observatory is right near the toll gates at the bottom of the Sydney Harbour Bridge (Bradfield Highway), an easy walk on Argyle Street to The Rocks on the other side of the Bradfield Highway.
Have a look at
Whereis for more detail.