Please note that as per the Institute’s policy, you need approval before you leave the country. If approval has not been granted and you leave the country, not only your student visa will be impacted but also you will be flagged by the Department of Immigration for not complying with your student visa and might be hard for you to come back, if you wish to do so.
Lastly, you mentioned about travelling around Sydney and Melbourne. Unfortunately you cannot do so. If you are absent from school for two weeks consecutively, you will be reported to the immigration.