If you are honestly interested in graphic design, you don't need to go to an art school. and i honestly strongly advised that you stay away from an art school if you want to do graphic design, if and only if you're not going to be attending the best art/design school for graphic design.
I say this because by going to an art/design school you're very limited to just being in an environment where you are around design/art students 24/7. and if you don't mind just being involved in design and art 24/7 then go for it, otherwise, it gets sickening and you just might end up turn off. That and art schools don't give big financial aid packages, as do regular universities. And in all honesty it is not worth getting into debt 100K just to go to a school and major in something that won't guarantee you a job. (they're more graphic designers available in todays market than needed)
while if you go to a major/regular university such as Carnegie Mellon University in Pennsylvania, who offers one of the best programs in the country, you have freedom to take more classes within regards to your liberal arts, and i honestly believe you get a more well rounded education, because you meet people from majors outside of design fields, and these people can become very beneficial if you end up changing your career in the future.