Yale is probably the most obvious one to target if you're looking into nonprofit/social enterprise, as it's got the most renowned rep for that.
Columbia -- you have an outside shot if you apply in their Early Decision round *and* you encounter a bit of good luck (assuming your essays, rec letters, interview, etc are stellar).
Berkeley, NYU, Duke -- you're in the mix; with a stellar app you should be competitive, although again the big obstacle is your GMAT
USC -- you have a reasonable shot of getting in
The GMAT is what's limiting you. You're just a smidgen below a lot of these school's middle 80% (which seems to creep up over time -- my hunch is that this upcoming year it's going to be 680-740 for most if not all the top 16 schools). Even with a 680 it can make a difference in your case.
If you can't bump up that GMAT, then all you can do is apply to these schools (I think you have enough of a shot that you should at least give them your best shot even with your current score), and just hope that there's enough luck on your side.