If I am in Sydney...

This answer is courtesy of Robert Walsh, of the Solar Theory Group, University of St. Andrews, Scotland

    Dear clever person,
 My Question is this: If I am in Sydney, Australia, as it so happens, I
 am, can the sun ever rise to the south of east? Would it be correct
 that the nearest to me this could happen is on our summer solstice on
 the tropic of capricorn?

I believe that it is no to the first question and yes to the second!! Let me explain.

Sydney is in New South Wales at a latitude of about 32 degrees. The tropic of capricorn is at approximately 23.5 degrees, this being the "lowest" latitude reached by the Sun in the Southern Hemisphere on the day of your summer solstice (20th December I think!!). Thus unfortunately for you in Sydney, the sun will never rise to the south of east (as you put it).

However, if you decided to travel north to just beyond the tropic of capricorn, then at the summer solstice the Sun would rise as you describe.

Hope this answers your question and I hope the weather is nice in Sydney. I live in Scotland and I can look out my window on the first winter snow-fall.

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Special Thanks to R. Walsh