I've looked at business schools throughout the Ivy League. I have a warm GPA, not hot, but have built a massive recent interest in business, finance, & economics. I will have a bachelor's degree in under a year. Transfer can be an option with the advantage you have taken of what your community has offered you. A rep. from HBS's hiring deck 'leaked' (however trustworthy) info about, unfortunately, the importance of the pedigree of the candidate's undergraduate degree. He said, though, that the college should maintain a generally neutral, unbiased outlook - sometimes that doesn't happen, but the outcome depends on each incident.
Stats look good for the schools, (salary avg. for an alumnus or alumna) except for the acceptance rates. Stanford - 7%. Harvard & Yale - both around 9%. Duke U & Cornell hover around 17%. Stanford has a 3-round acceptance cycle and they recommend applying on the first round if you are not seeking heavy competition, which comes in the second round. I wish you luck in this endeavor as well.
Where did you finish undergrad? I go to a state cc in middle GA that has a graduation rate of 13% (lower than the acceptance rate at Duke . . .) and does not seem to get my non-bleeding-heart sensibilities. It's too late for me to transfer hours. How are my odds? I am gauging my chances here, too.