It is possible to leave China by air, land, and sea and in all four compass directions, consult your guidebook for the best advice.Leaving Early
Many other exchange students particularly those from Germany or Italy seem to have made arrangements to leave early. Some students desired to be home for Christmas, well others seem to be operating on a different schedule. It may be worth your while to explore this further prior to arriving in China. This would allow you to start working sooner if you have already lined up a post degree job. If you whine loud enough you appear to be able to get your way, even having final exams emailed to you, for writing once back in your home country.
You likely have a six month student visa and a valid Chinese student card so you can use this to travel the width and breadth of China quite affordably. One downside is it will be January so the weather can be harsh in parts of China during the winter. There are however some famous winter festivals such as the one Harbin which starts on January 5th which can only be experienced in the appropriate season. If you are interest in working in China or Asia it is possible but it will still take effort, Mandarin skills are almost a necessity.Job Opportunities in China
Every Chinese classmate you will talk to will assure you how easy it is to get a job in China, however without solid Mandarin it is not that easy. In addition the problems with the Career Center and the inefficiency in providing information in English further complicate matters. There are some online jobsites and postings in English language newspapers and magazines in addition to on-campus recruiting events. I wrote an article about looking for work online.