Try cold-contacting local game companies just to see if you can come by and have a tour of the office. If nothing else, it will be a great learning experience and an opportunity to meet some people in the industry. In my case, I was extremely fortunate and after a day of observing and hanging out with the people at a company, I was offered an internship (I was told later that even though the company had the occasional intern, they never advertised internships).
I think the biggest thing that helped me out was that I was genuinely interested in everything I was seeing and being told. I was friendly and professional to everyone I met, and sincerely thanked everyone for their time. I appreciated the educational opportunity and wasn't harassing them asking for a job, and was honest about my technical abilities when I was asked. Just don't be discouraged. I emailed about 30 companies before getting a single response.