The George St area between Town Hall and Central can be a little rough very late at night. It's always busy though, so the usual precautions should see you stay out of trouble. Try to avoid Belmore Park on Eddy Avenue in front of Central Station at night as it seems to attract a lot of drug addicts and homeless people.
Central Bus Station isn't the best introduction to Sydney at any time of day, and is unpleasant after dark. If you are arriving late, have plans for how you are getting away safely.
internet cafes
There are many Internet cafes around the area, of every kind you could imagine. Small shops have terminals, internet stores advertise high speed and gaming access. World Square has coin operated terminals, along with a couple of the other shopping centres. Around central station there are several options although not on the station itself.
In addition the public libraries in the area offer Internet access.
Expect to pay a couple of dollars to check email, or try to get around $6 for an hour of usage.