UPDATE: check January events in Sydney this year.
Main event in Sydney in January is annual Sydney festival. Everybody can find what to do, what to listen, what to see. It is music, theater, dance, visual arts, talks. A lot of performance are free, including Festival First Night. Expect big crowd there if it is nice day. The above picture was taken last year during First Night concert. This year the gates to the domain and main stage were closed very early as was no place left for more people. In such case is worth check what is going around in Hide Park, Martin Place and I am sure it will be something interesting happening there too.
Another big event in January is nationwide event – Australia Day – on 26th of January. Check official web site about what is happening that day in city. Also it is good day to see fireworks in Darling Harbor in case you missed New Year Eve fireworks. Not such big, but still very spectacular.