Declining a Internship You've Already Accepted

I’ve recently been offered a small local magazine internship in my hometown. While I was applying for the internship, I also applied for some very big-name internship in NYC - whose deadlines are far from up. I felt rushed to accept the offer and thought it would be a good idea as a back-up plan. I signed no contract whatsoever, but did formally apply for the internship at my school. The magazine expects me to start in the fall. If for some out-of-the-blue reason I was to be offered an internship at one of the huge magazines, is it okay to decline the offer I already accepted? I don’t want to seem ungrateful, but I know that journalism is a tough industry and you need to do what you have to do to get ahead.