I must admit, when I was first choosing a college to go to my senior year of high school, I might as well have pasted as many prospects to my wall as possible and thrown darts blindly around the room until I hit one. Hamilton was my first dart pick, and upon visiting your campus, I fell in love immediately. Fate, it seems, enjoys playing darts. I had the tactical advantage of visiting campus in autumn, sitting in on several classes, and I enjoyed every minute of it. The students at Hamilton actually seem to enjoy going to class! As a prospective law and writing student, Hamilton emphasizes everything I want to get out of my educational experience. I have been all around the world, and of all the countries and cities I have been to, Hamilton, in Clinton, New York, is the only place that I have obsessed about incessantly upon hearing it’s name. Hamilton is perfect for me, so please, don’t prove fate wrong.
"I must admit, when I was first choosing a college to go to my senior year of high school, I might as well have pasted as many prospects to my wall as possible and thrown darts blindly around the room until I hit one"
Just remove this.. if you want to sound personal, be personal. Don't contrive something from the air.
"Hamilton was my first dart pick"
More of a reason to remove, it's poorly worded.
Don't make jokes I'd say. Be honest, be assertive, and be real. You're applying for an education about law and writing. If you're going for a laugh, at least make it about you and not your inability to choose a university to apply towards. No?
"I enjoyed every minute of it" what specifically.. I think they'll react better if you say specifically what you enjoyed (or pretended to enjoy). The professor's, the warmth of the student body around campus etc. etc.
"everything I want to get out of my educational experience" again, specifics
"only place that I have obsessed about incessantly upon hearing it’s name"
you obsessed about a university after hearing it's name? why?
"Hamilton is perfect for me, so please, don’t prove fate wrong." it comes off desperate, no?
sorry if i sound harsh. just trying to help you fix your issues.