Sure fireworks are banned in Canberra, and porn is available at the click of a button so you may think that there is no real need to go to Canberra anymore. Well there is, as a student there are plenty of things to do and see like Questacon which offers student entry deals and is not just for kids (although steer clear of this during school holidays), maybe go to the war memorial or visit parliament house.
The NSW Trainlink offers students return tickets to Canberra for about $30.00 and it gets you there from Central Station about 4 hours. See http://www.nswtrainlink.info
Generally you should be able to get accommodation for about $100 a night if you book a hotel through last minute, wotif or expedia. You can also see hostels, which will be considerably cheaper however ensure you have read the trip advisor reviews (http://www.tripadvisor.com.au) before booking a hostel as some places are not nice at all.