When is it best to travel to Sydney Australia?

(temperature and low rainfall)?

I've been to Sydney in November (their summer) and in June (their winter) and there wasn't a tremendous difference. Of course November was a few degrees warmer, but the rain was fairly consistent (it rained 2 days on both visits).
I would recommend going during their summer months, but it seemed much less hectic during their winter months.
Either way, have fun!
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The driest time of the year in Sydney is the second half of September into early October. That is when the Olympic Games were held for that very reason. The most exciting time to be in Sydney is January when the Festival of Sydney is on starting with the New Years fireworks over the Bridge and taking in the many free concerts in the Domain - Opera in the Park, Symphony Under the Stars, Jazz, Australia Day etc.

Spring and Autumn (Fall) are the pick, in my opinion. Not cold. Usually clear days (the Olympics were in September for a reason). Summer, particularly January and February, can be very hot and humid. If you want to swim go in March-early April (Autumn) when the water is still warm enough and there are no crowds on the beaches. If the heat does not worry you there is an arts festival for most of January, New Years Eve is spectacular and January is a buzzy time to be here.

Remember that our seasons are the reverse of the Northern Hemisphere.

All depends on what you intend to do whilst you are here. The summer months are very hot and humid, with the temp reaching 40 degrees some days. December and January are our hottest months, though it tends to rain a lot during nov/dec. The most comfortable periods for travelling are probably spring and autumn. The weather is decent and you still have sunny days, without it being too hot or cold.

However, note that our weather is quite variable. It may change drastically several times during the same day. We get heat waves, followed by cold days, periods of drought and then excessive rain. Or a combination of all of that all within 24 hours! :)

tentofield got it spot on.
Late October is storm season. June is always really windy.
January is very hot, most days are around 30 celcius at least, more if you are slightly inland (like Penrith) but the beach culture is in full swing. I would say about now is good, its been around 21 degrees up until mid OCtober.

Yeah, you should travel to Sydney in summer when the temperatures are mid-20 celsius and there is not much rainfall. Then you can enjoy the World's best beach, Bondi.