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Undergraduate GPA: 3.85 / 4.0 from a top-15 US University (Duke/Rice/Emory). My degree is in a non-economics social science discipline, though I received As in a few quantitative courses.
Graduate School: 2-year Masters Degree from a top European university (Cambridge/Oxford). Again, the subject was a non-economics social science discipline, but my thesis involved a heavy quantitative element and I received an award for my work in statistics.
GMAT: No score to report. I'm in the process of studying now, but need to be realistic about my potential score range. Having not studied basic math since high school, I would be happy with a score in the 660-700 range.
Work Experience: I spent one year as a Strategy Analyst in a large management consultancy and am currently entering my second year as an Analyst at a bulge-bracket investment bank. I have received top marks in all performance reviews and am confident that I will be able to secure strong recommendation letters as evidence of my achievements. All of my work experience has been abroad.
Motivation: I am seeking to do an MBA as a means of transitioning into the PE/VC space. Though my current job involves working with PE fund managers, I am not in a "traditional" M&A / Corporate Finance role and thus may not be viewed as having the requisite skills to land a job in a PE house. Also - as my previous degrees were not in an economics/finance/business discipline - I genuinely view an MBA as a great way to brush up on the fundamentals, meet fascinating, like-minded people and send a clear signal that I am a serious candidate despite my non-traditional academic background.
1) Based on the above, do I stand a chance of getting into any of the following programs: Harvard, MIT, Yale, Dartmouth, Wharton, NYU or Columbia? As my desired career is in an extremely competitive industry (and consdiering the cost of attedning B-school), I have decided that I will only enroll if I am granted admission to one of these programs. (Note that I need to be in New England for personal reasons). And what do you consider to be the cut-off GMAT score for these schools? Do I stand a chance with a 660-680 or will I need to break the 700 mark?
2) Is now the right time for me to apply? By the time I enroll, I will only have 3 years of work experience (though I will be in my late 20s and have differentited experience - i.e., studying and working abroad for five years). I am also aware that this is the most competitive admissions environment in some time, especially for those applying from financial services. The timing makes sense for personal reasons, but I am concerned that my chances will be diminished by the myriad newly-unemployed IBD Analysts with stellar credentials who will undoubtedly be applying this year.
You didn't mention key data like your gender, your cultural background, and your extracurricular leadership experiences, so it's hard for me to comment usefully. Your work experience sounds impressive but the switch from consulting to IB will need some explaining. If I were you, I would not state a PE/VC goalin your application. It's just a very common post-MBA goal to cite these days. You should aim for a 700, yes. But there are some applicants who might have a chance at some of the schools you mentioned with GMATs in the 660-700 range. I don't have the info to be able to tell you whether you're one of them.
My rough guess is that you may have a decent chance at schools like MIT, Yale, and NYU, but less of a chance at the others, especially HBS. If you will be in your late 20s by the time you enroll, then you had better apply now, despite the competitiveness of the admissions season. Aim for the first round.