I think your chances at the CMU and Berkeley programs you mentioned are good. You have excellent numbers and what appears to be some solid and interesting experiences relevant to your goals. Why are you unsure you'd be competitive at these programs?
Given your lack of work experience an MBA is less doable, since most schools like 2-3 years of experience. However, there are some exceptions--schools known for admitting large percentages of newbies like yourself. Rochester, Vanderbilt, CMU, and Illinois are all respected finance schools and all average at least 9% students with 1 year or less of work experience.
Thanks for your advice. I am unsure of whether I'll be competitive because I know my GPA isn't fantastic.
May I inquire about my chances for Princeton's MS in Finance, as well?