First paragraph is good but you haven't clearly and explicitly stated WHY. - why were you attracted to traveling and exploring different cultures? - the cuisine, the lifestyle, exposure, new experiences? what exactly appealed to you? - perhaps the world and it's multifarious ways of living?
The University experience is about both personal and academic growth. I truly believe that the International Student Exchange program will benefit me in both areas.
how will it benefit you - give a concrete example, exposure = knowledge? learning various cultures and values enhances you're perception of the world and encourages you to be a liberal thinker?
i like the ending of your 2nd paragraph - the way you tied it all together.
The granddaughter
" As the granddaughter of..." instead?
but I awakened in me a longing to learn and experience more about the land my family originates from
I find this to be an awkward phrase. "but it awakened in me ...."
It would have helped to post the prompt of this essay...
all in all a good essay. However your last paragraph doesn't powerfully tie in with you're desire to study abroad, try and work on making the ending of your essay as or even powerful than you're begining.
Edit and post again so we can critique:)